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Journal articles on the topic 'Exponential Family of distribution'

Author: Grafiati

Published: 28 June 2021

Last updated: 29 July 2025

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1

Awodutire, Phillip. "Statistical Properties and Applications of the Exponentiated Chen-G Family of Distributions: Exponential Distribution as a Baseline Distribution." Austrian Journal of Statistics 51, no. 2 (2022): 57–90. http://dx.doi.org/10.17713/ajs.v51i2.1245.

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In this work, the Exponentiated Chen-G family of distributions is studied by generalizing the Chen-G family of distributions through the introduction of an additional shape parameter. The mixture properties of the derived family are studied. Some statistical properties of the family were considered, including moments, entropies, moment generating function, order statistics, quantile function. The estimation of the parameters of the family of distributions was done using the maximum likelihood estimation method, considering complete and censored situations. Using the Exponential distribution as

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Mahmoud, Mahmoud Riad, Moshera A. M. Ahmad, and AzzaE Ismail. "T-Inverse Exponential Family Of Distributions." Journal of University of Shanghai for Science and Technology 23, no. 09 (2021): 556–72. http://dx.doi.org/10.51201/jusst/21/08495.

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Recently, several methods have been introduced to generate neoteric distributions with more exibility, like T-X, T-R [Y] and alpha power. The T-Inverse exponential [Y] neoteric family of distributons is proposed in this paper utilising the T-R [Y] method. A generalised inverse exponential (IE) distribution family has been established. The distribution family is generated using quantile functions of some dierent distributions. A number of general features in the T-IE [Y] family are examined, like mean deviation, mode, moments, quantile function, and entropies. A special model of the T-IE [Y] di

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Hussein, Mohamed, Howaida Elsayed, and Gauss M. Cordeiro. "A New Family of Continuous Distributions: Properties and Estimation." Symmetry 14, no. 2 (2022): 276. http://dx.doi.org/10.3390/sym14020276.

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We introduce a new flexible modified alpha power (MAP) family of distributions by adding two parameters to a baseline model. Some of its mathematical properties are addressed. We show empirically that the new family is a good competitor to the Beta-F and Kumaraswamy-F classes, which have been widely applied in several areas. A new extension of the exponential distribution, called the modified alpha power exponential (MAPE) distribution, is defined by applying the MAP transformation to the exponential distribution. Some properties and maximum likelihood estimates are provided for this distribut

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Chinazom, Odom Conleth, Nduka Ethelbert Chinaka, and Ijomah Maxwell Azubuike. "The T-Exponentiated Exponential{Frechet} Family of Distributions: Theory and Applications." Asian Journal of Probability and Statistics 23, no. 4 (2023): 8–25. http://dx.doi.org/10.9734/ajpas/2023/v23i4509.

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This article introduces a new family of Generalized Exponentiated Exponential distribution. Using the T-R{Y} framework, a new family of T-Exponentiated Exponential{Y} distributions named T-Exponentiated Exponential{Frechet} family of distributions is proposed. Some general properties of the family such as hazard rate function, quantile function, non-central moment, mode, mean absolute deviations and Shannon’s entropy are discussed. A new continuous univariate probability distribution which is a member of the T-Exponentiated Exponential{Frechet} family of distributions is introduced. From the g

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Awodutire, Phillip Oluwatobi, Oluwafemi Samson Balogun, Akintayo Kehinde Olapade, and Ethelbert Chinaka Nduka. "The modified beta transmuted family of distributions with applications using the exponential distribution." PLOS ONE 16, no. 11 (2021): e0258512. http://dx.doi.org/10.1371/journal.pone.0258512.

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In this work, a new family of distributions, which extends the Beta transmuted family, was obtained, called the Modified Beta Transmuted Family of distribution. This derived family has the Beta Family of Distribution and the Transmuted family of distribution as subfamilies. The Modified beta transmuted frechet, modified beta transmuted exponential, modified beta transmuted gompertz and modified beta transmuted lindley were obtained as special cases. The analytical expressions were studied for some statistical properties of the derived family of distribution which includes the moments, moments

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Block, Henry W., Naftali A. Langberg, and Thomas H. Savits. "A MIXTURE OF EXPONENTIAL AND IFR GAMMA DISTRIBUTIONS HAVING AN UPSIDEDOWN BATHTUB-SHAPED FAILURE RATE." Probability in the Engineering and Informational Sciences 26, no. 4 (2012): 573–80. http://dx.doi.org/10.1017/s0269964812000204.

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We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

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Makubate, Boikanyo, Broderick O. Oluyede, Gofaone Motobetso, Shujiao Huang, and Adeniyi F. Fagbamigbe. "The Beta Weibull-G Family of Distributions: Model, Properties and Application." International Journal of Statistics and Probability 7, no. 2 (2018): 12. http://dx.doi.org/10.5539/ijsp.v7n2p12.

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A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series ex

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Reyes, Jimmy, Barry C. Arnold, Yolanda M. Gómez, Osvaldo Venegas, and Héctor W. Gómez. "Modified Bimodal Exponential Distribution with Applications." Axioms 14, no. 6 (2025): 461. https://doi.org/10.3390/axioms14060461.

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In this paper, we introduce a new distribution for modeling bimodal data supported on non-negative real numbers and particularly suited with an excess of very small values. This family of distributions is derived by multiplying the exponential distribution by a fourth-degree polynomial, resulting in a model that better fits the shape of the second mode of the empirical distribution of the data. We study the general density of this new family of distributions, along with its properties, moments, and skewness and kurtosis coefficients. A simulation study is performed to estimate parameters by th

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Abdullahi, J., S. U. Gulumbe, U. Usman, and A. I. Garba. "The Transform-Transformer Approach: Unveiling the Odd Transmuted Rayleigh-X Family of Distributions." International Journal of Science for Global Sustainability 9, no. 2 (2023): 85–98. http://dx.doi.org/10.57233/ijsgs.v9i2.462.

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The paper presents a novel class (family) of statistical distributions termed Odd Transmuted Rayleigh-X (OTR-X) that was created through a transform-transformer (T-X) approach. The CDF and PDF of the OTR-X family were derived. The available statistical literature studied earlier highlighted that almost all generalized distributions (in which one or more parameters were added) performed well and have better presentation of data than their counterparts with less number of parameters. This has motivated us to developed new family that is capable of producing new distributions. The research paper

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Badmus, N. I., Olanrewaju Faweya, and K. A. Adeleke. "Generalized Beta-Exponential Weibull Distribution and its Applications." Journal of Statistics: Advances in Theory and Applications 24, no. 1 (2020): 1–33. http://dx.doi.org/10.18642/jsata_7100122158.

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In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entro

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Louzada, Francisco, Vitor Marchi, and James Carpenter. "The Complementary Exponentiated Exponential Geometric Lifetime Distribution." Journal of Probability and Statistics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/502159.

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We proposed a new family of lifetime distributions, namely, complementary exponentiated exponential geometric distribution. This new family arises on a latent competing risk scenario, where the lifetime associated with a particular risk is not observable but only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments,rth moment of theith order statistic, mean residual lifetime, and modal value. Inference is i

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Binod, Kumar Sah. "Quadratic-Exponential Distribution." MATHEMATICS EDUCATION LVI, no. 1, March 2022 (2022): 1–17. https://doi.org/10.5281/zenodo.6381529.

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             In this paper, we introduce a new member of family of continuous probability distributions which is based on the product of quadratic and exponential functions and hence, we named it ‘Quadratic-Exponential Distribution’. Probability density function, probability distribution function and moment generating function of this distribution have been obtained. Moments about origin and hence, the first four central moments of the proposed distribution have been derived. The hazard rate function and the mean residual life function of the prop

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Adisa, Agbona Anthony, Odukoya Elijah Ayooluwa, Amalare Asimi, and Ayeni Taiwo Michael. "Exponential-Gamma-Rayleigh Distribution: Theory and Properties." Asian Journal of Probability and Statistics 27, no. 3 (2025): 134–44. https://doi.org/10.9734/ajpas/2025/v27i3730.

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The use of traditional probability models to forecast real-world events is causing growing dissatisfaction among scholars. One of the motives could be the tail characteristics and goodness of fit metrics has a constraining tendency. Subsequently, there has been a significant increase in the generalisation of well-known probability distributions in recent years. The challenge is finding families versatile enough to fit both skewed and symmetric data. It is essential to understand that most generalised distributions described in the literature were developed using the generalised transformed tra

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Ghanam ahmed mahdi and Mundher abdaullah khaleel. "The Hybrid Odd Exponential-Exponential Distribution: Statistical Properties and Applications." Tikrit Journal of Administrative and Economic Sciences 20, no. 67, part 1 (2024): 457–73. http://dx.doi.org/10.25130/tjaes.20.67.1.23.

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In this paper, we study a new statistical distribution called the hybrid odd exponential-exponential distribution (HOE-E distribution for short) we the aim of applying it to real data sets. This new distribution appears as a sub-model of the larger HOEE-Φ family in (Mahdi et al., 2024). We explore many mathematical and statistical properties of this distribution such as the series expansion of the PDF, the quantile function, moments and their generating function, incomplete moments, the shape of the PDF, and the shape of the hazard rate function, order statistics, and parameter estimation usin

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Kalt, Hazim Ghdhaib. "A New Family of Continuous Distributions with Applications." Statistics, Optimization & Information Computing 12, no. 6 (2024): 1710–24. http://dx.doi.org/10.19139/soic-2310-5070-2144.

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This article introduces a novel set of optimizing probability distributions known as the Survival Power-G (SP-G) family, which employs a specific approach to introduce an additional parameter with the survival function of the original distributions. The utilization of this family enhances the modelling capabilities of diverse existing continuous distributions. By applying this approach to the single-parameter exponential distribution, a new two-parameter Survival Power-Exponential (SP-E) distribution is generated. The statistical characteristics of this fresh distribution and the maximum likel

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蔡, 正浩. "Higher Order Moments of Exponential Family Distribution." Pure Mathematics 13, no. 03 (2023): 437–44. http://dx.doi.org/10.12677/pm.2023.133048.

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17

Ghorbanpour, Samereh, Rahim Chinipardaz, and Seyed Mohammad Reza Alavi. "Form-Invariance of the Non-Regular Exponential Family of Distributions." Revista Colombiana de Estadística 41, no. 2 (2018): 157–72. http://dx.doi.org/10.15446/rce.v41n2.62233.

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The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular fami

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18

Sadiq, Ibrahim Abubakar, S. I. S. Doguwa, Abubakar Yahaya, and Jamilu Garba. "NEW GENERALIZED ODD FRÉCHET-ODD EXPONENTIAL-G FAMILY OF DISTRIBUTION WITH STATISTICAL PROPERTIES AND APPLICATIONS." FUDMA JOURNAL OF SCIENCES 7, no. 6 (2023): 41–51. http://dx.doi.org/10.33003/fjs-2023-0706-2096.

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A new lifetime continuous probability distribution called the new Generalized Odd Fréchet-Odd-Exponential-G Family of Distribution is developed using the principle of Alzaatreh. The developed distribution is flexible for studying positive real-life datasets. The statistical properties related to this family are obtained. The parameters of the family were estimated by using a technique of maximum likelihood. A NewGeneralized Odd Fréchet-Odd-Exponential-Weibull model is introduced. This distribution was fitted with a set of lifetime data. A Monte Carlo simulation is applied to test the consisten

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Ampadu, Clement Boateng. "Further Developments on the (EG) Exponential-MIR Class of Distributions." Journal of Advanced Research in Biotechnology 3, no. 2 (2018): 1–5. http://dx.doi.org/10.15226/2475-4714/3/2/00137.

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The Modified Inverse Rayleigh (MIR) distribution appeared in [Khan, M. S. (2014).Modified inverse Rayleigh distribution. International Journal of Computer Applications, 87(13):28–33] who got some theoretical properties of this distribution, and in[Nasiru, S., Mwita, P. N. and Ngesa, O. (2017). Exponentiated Generalized Exponential Dagum Distribution. Journal of King Saud University- Science, In Press] they introduced the (EG) Exponential-X class of distributions and obtained some theoretical properties with application. By assuming the random variable X follows the MIR distribution, some theor

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Abdulkadir, Dr Sauta Saidu, J. Jerry, and T. G. Ieren. "STATISTICAL PROPERTIES OF LOMAX-INVERSE EXPONENTIAL DISTRIBUTION AND APPLICATIONS TO REAL LIFE DATA." FUDMA JOURNAL OF SCIENCES 4, no. 2 (2020): 680–94. http://dx.doi.org/10.33003/fjs-2020-0402-435.

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This paper proposes a Lomax-inverse exponential distribution as an improvement on the inverse exponential distribution in the form of Lomax-inverse Exponential using the Lomax generator (Lomax-G family) with two extra parameters to generalize any continuous distribution (CDF). The probability density function (PDF) and cumulative distribution function (CDF) of the Lomax-inverse exponential distribution are defined. Some basic properties of the new distribution are derived and extensively studied. The unknown parameters estimation of the distribution is done by method of maximum likelihood esti

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Sudsila, Pupe, Ampai Thongteeraparp, Sirinapa Aryuyuen, and Winai Bodhisuwan. "The Generalized Distributions on the Unit Interval based on the T-Topp-Leone Family of Distributions." Trends in Sciences 19, no. 19 (2022): 6186. http://dx.doi.org/10.48048/tis.2022.6186.

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The Topp-Leone (TL) distribution is introduced by Topp and Leone [1]. Its probability density function is a simple function with only one parameter. Even though the TL distribution has been discussed and applied in many research fields, but there is a limitation about its shape. In this article, we propose the T-TL family of distributions using quantile function of family of distributions to generate generalized TL distributions including the Weibull-TL{exponential}, the log-logistic-TL{exponential}, the logistic-TL{extreme value}, the exponential-TL{log-logistic} and the normal-TL{logistic} d

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Kajuru, Jibril Yahaya, Hussaini Dikko Garba, Aminu Mohammed Suleiman, and Aliyu Fulatan Ibrahim. "The Generalized Gompertz-G Family of Distributions: Statistical Properties and Applications." UMYU Scientifica 3, no. 1 (2024): 120–28. http://dx.doi.org/10.56919/usci.2431.014.

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This research aimed at presenting a new statistical model called the Generalized Gompertz-G family of distribution via the method of Alzaatreh, which introduces additional shape parameters for any baseline distribution. We investigate various mathematical aspects of this model, explicitly deriving properties such as moments, moment-generating function, survival function, hazard function, entropies, quantile function, and order statistics distribution. We explore a particular member of this family of distributions, the Generalized Gompertz-Exponential Distribution (GGED), by defining its proper

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Tzougas, George, and Dimitris Karlis. "AN EM ALGORITHM FOR FITTING A NEW CLASS OF MIXED EXPONENTIAL REGRESSION MODELS WITH VARYING DISPERSION." ASTIN Bulletin 50, no. 2 (2020): 555–83. http://dx.doi.org/10.1017/asb.2020.13.

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AbstractRegression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become increasingly popular in many insurance settings including non-life insurance. Mixed Exponential models can be considered as a natural choice for the distribution of heavy-tailed claim sizes since their tails are not exponentially bounded. This paper is concerned with introducing a general family of mixed Exponential regression models with varying dispersion which can efficiently capture the tail behaviour of losses. Our main achievement is that we p

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Chesneau, Christophe, Lishamol Tomy, Meenu Jose, and Kuttappan Vallikkattil Jayamol. "Odd Exponential-Logarithmic Family of Distributions: Features and Modeling." Mathematical and Computational Applications 27, no. 4 (2022): 68. http://dx.doi.org/10.3390/mca27040068.

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This paper introduces a general family of continuous distributions, based on the exponential-logarithmic distribution and the odd transformation. It is called the “odd exponential logarithmic family”. We intend to create novel distributions with desired qualities for practical applications, using the unique properties of the exponential-logarithmic distribution as an initial inspiration. Thus, we present some special members of this family that stand out for the versatile shape properties of their corresponding functions. Then, a comprehensive mathematical treatment of the family is provided,

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Adekunle, Kolawole Ismail, Yahaya Abubakar, Sani Ibrahim Doguwa, and Aliyu Yakubu. "KUMARASWAMY TYPE II GENERALIZED TOPP-LEONE-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS." FUDMA JOURNAL OF SCIENCES 8, no. 6 (2024): 186–95. https://doi.org/10.33003/fjs-2024-0806-2747.

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In the field of reliability theory, practitioners have been working assiduously in recent years to propose new families of continuous probability distributions that extend the standard theoretical distribution that is currently in use. They have done this by hybridizing two or more probability models or by introducing one or more parameters to get more flexibility in fitting data from a variety of fields, including the environmental, economics, finance, and medical sciences. The T-X approach was used to establish the Kumaraswamy Type II Generalized Topp-Leone-G (KwT2GTL-G) family, which extend

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El-Morshedy, Mahmoud, and Mohamed Eliwa. "A bivariate probability generator for the odd generalized exponential model: Mathematical structure and data fitting." Filomat 38, no. 3 (2024): 1109–33. http://dx.doi.org/10.2298/fil2403109e.

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The generalized exponential (GE) distribution is the well-established generalization of the exponential distribution in statistical literature. Tahir et al. (2015) proposed a flexible probability generator called the odd generalized exponential-G (OGE-G) family of distributions. In this article, we propose a bivariate extension of the OGE-G class, in the so-called the bivariate odd generalized exponential-G (BOGE-G) family of distributions, whose marginal distributions are OGE-G families. Important mathematical and statistical properties of the BOGE-G family including joint density function wi

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Mian, Rajibul, and Sudhir Paul. "Tests of exponentiality against some parametric over/under-dispersed life time models." Acta et Commentationes Universitatis Tartuensis de Mathematica 21, no. 2 (2017): 207–23. http://dx.doi.org/10.12697/acutm.2017.21.14.

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We develop tests of goodness of fit of the exponential model against some over/under dispersion family of distributions. In particular, we develop 3 score test statistics and 3 likelihood ratio statistics. These are (S1, L1), (S2, L2), and (S3, L3) based on a general over-dispersed family of distributions, two specic over/under dispersed exponential models, namely, the gamma and the Weibull distributions, respectively. A simulation study shows that the statistics S3 and L3 have best overall performance, in terms of both, level and power. However, the statistic L3 can be liberal in some instanc

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Abouelmagd, T. H. M. "The Logarithmic Burr-Hatke Exponential Distribution for Modeling Reliability and Medical Data." International Journal of Statistics and Probability 7, no. 5 (2018): 73. http://dx.doi.org/10.5539/ijsp.v7n5p73.

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In this work, we introduced a new one-parameter exponential distribution. Some of its structural properties are derived% \textbf{.} The maximum likelihood method is used to estimate the model parameters by means of numerical Monte Carlo simulation study. The justification for the practicality of the new lifetime model is based on the wider use of the exponential model. The new model can be viewed as a mixtureof the exponentiated exponential distribution. It can also be considered as a suitable model for fitting right skewed data.\textbf{\ }We prove empirically the importance and flexibility of

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Semary, H. E., Zawar Hussain, Walaa A. Hamdi, Maha A. Aldahlan, Ibrahim Elbatal, and Vasili B. V. Nagarjuna. "Alpha–beta-power family of distributions with applications to exponential distribution." Alexandria Engineering Journal 100 (August 2024): 15–31. http://dx.doi.org/10.1016/j.aej.2024.05.024.

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Layla Abdul Jaleel Mohsin. "A New Family of Distributions with an Application to Exponentially Distribution." Communications on Applied Nonlinear Analysis 31, no. 4s (2024): 135–46. http://dx.doi.org/10.52783/cana.v31.832.

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This paper introduces a new continuous distribution family called the Alpha logarithm family, which is a new modelling strategy for fitting data subject to univariate continuous distributions. This is achieved by introducing an additional parameter for greater flexibility using a single-parameter Natural logarithm transformation which can enhance some of the modeling capabilities of some Parental Continuous Distributions: This technique was applied to the exponential distribution to obtain a new two-parameter distribution, and the changes that occurred in the exponential distribution were obse

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Bilal, Muhammad, Muhammad Mohsin, and Muhammad Aslam. "Weibull-Exponential Distribution and Its Application in Monitoring Industrial Process." Mathematical Problems in Engineering 2021 (March 26, 2021): 1–13. http://dx.doi.org/10.1155/2021/6650237.

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This paper presents a new Weibull family of distributions. The compatibility of the newly developed class is justified through its application in the field of quality control using Weibull-exponential distribution, a special case of the proposed family. In this paper, an attribute control chart using Weibull-exponential distribution is developed. The estimations of the model parameters and the proposed chart parameters are performed through the methods of maximum likelihood and average run-length. The significance of the proposed model is demonstrated using a simulation study and real-life pro

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Gómez-Déniz, Emilio, Yuri A. Iriarte, Yolanda M. Gómez, Inmaculada Barranco-Chamorro, and Héctor W. Gómez. "Statistical Inference for a General Family of Modified Exponentiated Distributions." Mathematics 9, no. 23 (2021): 3069. http://dx.doi.org/10.3390/math9233069.

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In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile function, moments, stochastic ordering, Poisson mixture with our proposal as the mixing distribution, order statistics, tail behavior and estimates of parameters. We highlight the particular model based on the classical exponential distribution, which is an alternative to the exponentiated exponential, gamm

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Cao, Limei, Huafei Sun, and Xiaojie Wang. "The geometric structures of the Weibull distribution manifold and the generalized exponential distribution manifold." Tamkang Journal of Mathematics 39, no. 1 (2008): 45–51. http://dx.doi.org/10.5556/j.tkjm.39.2008.44.

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Investigating the geometric structures of the distribution manifolds is a basic task in information geometry. However, by so far, most works are on the distribution manifolds of exponential family. In this paper, we investigate two non-exponential distribution manifolds —the Weibull distribution manifold and the generalized exponential distribution manifold. Then we obtain their geometric structures.

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McLeish, Don L. "Bounded Relative Error Importance Sampling and Rare Event Simulation." ASTIN Bulletin 40, no. 1 (2010): 377–98. http://dx.doi.org/10.2143/ast.40.1.2049235.

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AbstractWe consider estimating tail events using exponential families of importance sampling distributions. When the cannonical sufficient statistic for the exponential family mimics the tail behaviour of the underlying cumulative distribution function, we can achieve bounded relative error for estimating tail probabilities. Examples of rare event simulation from various distributions including Tukey's g&h distribution are provided.

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Iwasaki, Masakazu, and Hiroe Tsubaki. "A new bivariate distribution in natural exponential family." Metrika 61, no. 3 (2005): 323–36. http://dx.doi.org/10.1007/s001840400348.

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Baharith, Lamya A., Kholod M. AL-Beladi, and Hadeel S. Klakattawi. "The Odds Exponential-Pareto IV Distribution: Regression Model and Application." Entropy 22, no. 5 (2020): 497. http://dx.doi.org/10.3390/e22050497.

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This article introduces the odds exponential-Pareto IV distribution, which belongs to the odds family of distributions. We studied the statistical properties of this new distribution. The odds exponential-Pareto IV distribution provided decreasing, increasing, and upside-down hazard functions. We employed the maximum likelihood method to estimate the distribution parameters. The estimators performance was assessed by conducting simulation studies. A new log location-scale regression model based on the odds exponential-Pareto IV distribution was also introduced. Parameter estimates of the propo

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Zubair, Muhammad, Ayman Alzaatreh, Gauss Cordeiro, M. H. Tahir, and Muhammad Mansoor. "On generalized classes of exponential distribution using T-X family framework." Filomat 32, no. 4 (2018): 1259–72. http://dx.doi.org/10.2298/fil1804259z.

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We introduce new generalized classes of exponential distribution, called T-exponential {Y} class using the quantile functions of well-known distributions. We derive some general mathematical properties of this class including explicit expressions for the quantile function, Shannon entropy, moments and mean deviations. Some generalized exponential families are investigated. The shapes of the models in these families can be symmetric, left-skewed, right-skewed and reversed-J, and the hazard rate can be increasing, decreasing, bathtub, upside-down bathtub, J and reverse-J shaped. Two real data se

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Bashiru, Kehinde Adekunle, Taiwo Adetola Ojurongbe, Lawal Sola, Nureni Olawale Adeboye, and Habeeb Abiodun Afolabi. "Double-Exponential-X Family of Distributions: Properties and Applications." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 3 (2023): 437–49. http://dx.doi.org/10.30526/36.3.3377.

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A new family of distribution named Double-Exponential-X family is proposed. The proposed family is generated from the double exponential distribution. The forms of the probability densities and hazard functions of two distinct subfamilies of the proposed family are examined and reported. Generalproperties such as moment, survival, order statistics, probability weighted moments and quartile functions of the models are investigated. A sub family of the developed family of double –Exponential-X family of the distribution known as double-Exponential-Pareto distribution was used to fit a real life

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39

Rao, R. Prabhakar, and B. C. Sutradhar. "A Global Test for the Goodness of Fit of Generalized Linear Models : An Estimating Equation Approach." Calcutta Statistical Association Bulletin 56, no. 1-4 (2005): 251–82. http://dx.doi.org/10.1177/0008068320050514.

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Summary Generalized linear models are used to analyze a wide variety of discrete and continuous data with possible overdispersion under the assumption that the data follow an exponential family of distributions. The violation of this assumption may have adverse effects on the statistical inferences. The existing goodness of fit tests for checking this assumption are valid only for a standard exponential family of distributions with no overdispersion. In this paper, we develop a global goodness of fit test for the general exponential family of distributions which may or may not contain overdisp

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Abdullahi, Usman Aliyu, Ahmad Abubakar Suleiman, Aliyu Ismail Ishaq, Abubakar Usman, and Aminu Suleiman. "The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data." Journal of Statistical Modelling and Analytics 3, no. 2 (2021): 65–80. http://dx.doi.org/10.22452/josma.vol3no2.4.

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Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using tw

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Morad Ahmad and Mohammad Abdel-Moniem Amleh. "A New Method for Generating Continuous Distributions with Applications." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5981. https://doi.org/10.29020/nybg.ejpam.v18i2.5981.

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In this paper, a new modifying method has been introduced by adding an extra parameter to generate a new family of distributions that has more flexibility and better model fitting. A special case has been considered; the exponential distribution. All the main properties of the new modified exponential distribution are derived, including the CDF, PDF, and quantile function. The maximum likelihood estimation method is used to estimate unknown parameters. The modified exponential distribution has been applied to two-lifetime data sets to illustrate its efficiency.

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Bleed, Salma Omar. "NEW EXPONENTIAL CUMULATIVE HAZARD METHOD FOR GENERATING CONTINUOUS FAMILY DISTRIBUTIONS." مجلة الجامعة الأسمرية: العلوم التطبيقية 5, no. 1 (2020): 106–22. http://dx.doi.org/10.59743/aujas.v5i1.1646.

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The article aims to expand the use of the cumulative hazard function and cumulative generalized exponential distribution of Gupta and Kunda (1999) for introducing a new method for generating families from continuous distributions called the Exponential Cumulative Hazard (ECH) method. It's providing some of well-known methods and distributions embedded within the proposed method. New 5- parameter uniform distributions with 3-shape parameters and bathtub hazard function are introduced as a practical example to support the proposed method. Finally, application on real data-set is provided.

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Al-Babtain, Abdulhakim A., Mohammed K. Shakhatreh, Mazen Nassar, and Ahmed Z. Afify. "A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications." Mathematics 8, no. 8 (2020): 1345. http://dx.doi.org/10.3390/math8081345.

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In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of

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Chaudhary, Arun Kumar, Lal Babu Sah Telee, and Vijay Kumar. "Inverse Exponentiated Odd Lomax Exponential Distribution: Properties and Applications." Nepalese Journal of Statistics 6, no. 01 (2022): 29–50. http://dx.doi.org/10.3126/njs.v6i01.50801.

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Background: New family of distributions has important functions in generalization of distributions by modifying some existing distributions for getting more flexible irrespective to applied and practical view point. The Inverse Exponentiated Odd Lomax Exponential Distribution (IEOLE) having four parameters is suggested. Proposed model is based on T-X family of distribution which is the extended form of beta-generated distribution. Based on the LSE, MLE, and CVM methods, the parameters of the proposed distribution are estimated. Different model validation criteria and model comparisons are done

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Mohammad, Shahid. "X-exponential-G Family of Distributions With Applications." International Journal of Statistics and Probability 13, no. 1 (2024): 40. http://dx.doi.org/10.5539/ijsp.v13n1p40.

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A new family of continuous distributions called the X-exponential-G (XE-G) family is proposed. Explicit expressions are derived for the ordinary and incomplete moments, generating functions, mean deviation about the mean and median, Shannon and R\&#39;{e}nyi entropies, and order statistics of this new family. Estimation of the parameters of the new family is done using the method of maximum likelihood. Assessment of the performance of the maximum likelihood estimates is carried out through a simulation study using the quantile function of the XE-G distribution. The usefulness of this new f

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Marshall, Albert W., and Ingram Olkin. "Bivariate life distributions from Pólya's urn model for contagion." Journal of Applied Probability 30, no. 3 (1993): 497–508. http://dx.doi.org/10.2307/3214760.

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Shock models based on Poisson processes have been used to derive univariate and multivariate exponential distributions. But in many applications, Poisson processes are not realistic models of physical shock processes because they have independent increments; expanded models that allow for possibly dependent increments are of interest. In this paper, univariate and bivariate Pólya urn schemes are used to derive models of shock sources. The life distributions obtained from these models form a large parametric family that includes the exponential distribution. Even in the univariate case these li

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Marshall, Albert W., and Ingram Olkin. "Bivariate life distributions from Pólya's urn model for contagion." Journal of Applied Probability 30, no. 03 (1993): 497–508. http://dx.doi.org/10.1017/s0021900200044259.

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Shock models based on Poisson processes have been used to derive univariate and multivariate exponential distributions. But in many applications, Poisson processes are not realistic models of physical shock processes because they have independent increments; expanded models that allow for possibly dependent increments are of interest. In this paper, univariate and bivariate Pólya urn schemes are used to derive models of shock sources. The life distributions obtained from these models form a large parametric family that includes the exponential distribution. Even in the univariate case these li

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Pang, Liyuan, Weizhong Tian, Tingting Tong, and Xiangfei Chen. "Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications." Modelling 2, no. 4 (2021): 776–94. http://dx.doi.org/10.3390/modelling2040041.

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In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. M

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Chaudhary, Arun Kumar, and Vijay Kumar. "Half Cauchy-Modified Exponential Distribution: Properties and Applications." Nepal Journal of Mathematical Sciences 3, no. 1 (2022): 47–58. http://dx.doi.org/10.3126/njmathsci.v3i1.44125.

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A new distribution having three parameters using half Cauchy family of distribution named half Cauchy modified exponential distribution is deliberated and studied in this work. Its mathematical and statistical properties are examined. Model parameters of novel distribution are evaluated using least-square, maximum likelihood and Cramer-Von-Mises estimations approaches. R programming software is applied to carry out all of the calculations. To evaluate the new distribution's application and goodness-of-fit test, an actual data set is studied for illustration. The suggested new distribution is p

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Odeyale, Abideen Babatunde, Shehu Usman Gulumbe, Usman Umar, and Kazeem Olalekan Aremu. "New Odd Generalized Exponentiated Exponential-G Family of Distributions." UMYU Scientifica 2, no. 4 (2023): 56–64. http://dx.doi.org/10.56919/usci.2324.007.

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In the last decades, many researchers have developed new methods for generating families of distributions. These generators are obtained by adding one or more extra shape parameter(s) to the baseline distribution to achieve more flexibility for modelling real lifetime data sets. The additional parameter(s) has been proven useful by obtaining tail properties and improving the analysis from the goodness-of-fit for the families of distributions under study. In this paper, we proposed a new family of distributions called the New Odd Generalized Exponentiated Exponential-G Family of Distributions.

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