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Journal articles on the topic 'Generalized modified Weibull distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Alizadeh, Morad, Muhammad Nauman Khan, Mahdi Rasekhi, and G.G Hamedani. "A New Generalized Modified Weibull Distribution." Statistics, Optimization & Information Computing 9, no. 1 (January 22, 2021): 17–34. http://dx.doi.org/10.19139/soic-2310-5070-1014.

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We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer's $G$--function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as evidenced via goodness--of--fit tests

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2

Cordeiro, Gaussm, Abdus Saboor, Muhammad Khan, and Serge Provost. "The transmuted generalized modified Weibull distribution." Filomat 31, no. 5 (2017): 1395–412. http://dx.doi.org/10.2298/fil1705395c.

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Canada EM provost@stats.uwo.ca AU Ortega Edwinm M. AF Universidade de S?o Paulo, Departamento de Ci?ncias Exatas, Piracicaba, Brazil EM edwin@usp.br KW Generalized modifiedWeibull distribution % Goodness-of-fit statistic % Lifetime data % Transmuted family % Weibull distribution KR nema A profusion of new classes of distributions has recently proven useful to applied statisticians working in various areas of scientific investigation. Generalizing existing distributions by adding shape parameters leads to more flexible models. We define a new lifetime model called the transmuted generalized modified Weibull distribution from the family proposed by Aryal and Tsokos [1], which has a bathtub shaped hazard rate function. Some structural properties of the new model are investigated. The parameters of this distribution are estimated using the maximum likelihood approach. The proposed model turns out to be quite flexible for analyzing positive data. In fact, it can provide better fits than related distributions as measured by the Anderson-Darling (A*) and Cram?r-von Mises (W*) statistics, which is illustrated by applying it to two real data sets. It may serve as a viable alternative to other distributions for modeling positive data arising in several fields of science such as hydrology, biostatistics, meteorology and engineering.

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3

Oluyede, Broderick, Shujiao Huang, and Tiantian Yang. "A New Class of Generalized Modified Weibull Distribution with Applications." Austrian Journal of Statistics 44, no. 3 (October 14, 2015): 45–68. http://dx.doi.org/10.17713/ajs.v44i3.36.

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A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented.

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Ahmad, Zubair, and Brikhna Iqbal. "Generalized Flexible Weibull Extension Distribution." Circulation in Computer Science 2, no. 4 (May 20, 2017): 68–75. http://dx.doi.org/10.22632/ccs-2017-252-11.

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In this article, a four parameter generalization of the flexible Weibull extension distribution so-called generalized flexible Weibull extension distribution is studied. The proposed model belongs to T-X family of distributions proposed by Alzaatreh et al. [5]. The suggested model is much flexible and accommodates increasing, unimodal and modified unimodal failure rates. A comprehensive expression of the numerical properties and the estimates of the model parameters are obtained using maximum likelihood method. By appropriate choice of parameter values the new model reduces to four sub models. The proposed model is illustrated by means of three real data sets.

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5

Aryal, Gokarna, and Ibrahim Elbatal. "On the Exponentiated Generalized Modified Weibull Distribution." Communications for Statistical Applications and Methods 22, no. 4 (July 31, 2015): 333–48. http://dx.doi.org/10.5351/csam.2015.22.4.333.

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6

Abdelall, Yassmen Y. "The odd generalized exponential modified Weibull distribution." International Mathematical Forum 11 (2016): 943–59. http://dx.doi.org/10.12988/imf.2016.6793.

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7

O. Oluyede, Broderick, Huybrechts F. Bindele, Boikanyo Makubate, and Shujiao Huang. "A New Generalized Log-logistic and Modified Weibull Distribution with Applications." International Journal of Statistics and Probability 7, no. 3 (April 17, 2018): 72. http://dx.doi.org/10.5539/ijsp.v7n3p72.

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A new generalized distribution called the {\em log-logistic modified Weibull} (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and R\'enyi entropy are derived. Model parameters are estimated based on the method of maximum likelihood. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

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8

Carrasco, Jalmar M. F., Edwin M. M. Ortega, and Gauss M. Cordeiro. "A generalized modified Weibull distribution for lifetime modeling." Computational Statistics & Data Analysis 53, no. 2 (December 2008): 450–62. http://dx.doi.org/10.1016/j.csda.2008.08.023.

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9

Merovci, Faton, and Ibrahim Elbatal. "A New Generalized of Exponentiated Modified Weibull Distribution." Journal of Data Science 13, no. 2 (April 8, 2021): 213–40. http://dx.doi.org/10.6339/jds.201504_13(2).0001.

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10

Shahzad, Mirza Naveed, Ehsan Ullah, and Abid Hussanan. "Beta Exponentiated Modified Weibull Distribution: Properties and Application." Symmetry 11, no. 6 (June 12, 2019): 781. http://dx.doi.org/10.3390/sym11060781.

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One of the most prominent statistical distributions is the Weibull distribution. The recent modifications in this distribution have enhanced its application but only in specific fields. To introduce a more generalized Weibull distribution, in this work beta exponentiated modified Weibull distribution is established. This distribution consolidate the exponential, skewed and symmetric shapes into one density. The proposed distribution also contains nineteen lifetime distributions as a special case, which shows the flexibility of the distribution. The statistical properties of the proposed model are derived and discussed, including reliability analysis and order statistics. The hazard function of the proposed distribution can have a unimodal, decreasing, bathtub, upside-down bathtub, and increasing shape that make it effective in reliability analysis. The parameters of the proposed model are evaluated by maximum likelihood and least squares estimation methods. The significance of the beta exponentiated modified Weibull distribution for modeling is illustrated by the study of real data. The numerical study indicates that the new proposed distribution gives better results than other comparable distributions.

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11

Saboori, Hadi, Ghobad Barmalzan, and Seyyed Masih Ayat. "Generalized Modified Inverse Weibull Distribution: Its Properties and Applications." Sankhya B 82, no. 2 (February 15, 2019): 247–69. http://dx.doi.org/10.1007/s13571-018-0182-1.

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12

Bagheri, S. F., E. Bahrami Samani, and M. Ganjali. "The generalized modified Weibull power series distribution: Theory and applications." Computational Statistics & Data Analysis 94 (February 2016): 136–60. http://dx.doi.org/10.1016/j.csda.2015.08.008.

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13

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 (August 9, 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 the new model in modelingcancer patients data, the new model provides adequate fits as compared to other related models with small values for $W^{\ast }$\ \ and $A^{\ast }$. The new model is much better than the Modified beta-Weibull, Weibull, exponentiated transmuted generalized Rayleig, the transmuted modified-Weibull, and transmuted additive Weibull models in modeling cancer patients data. We are also motivated to introduce this new model because it has only one parameter and we can generate some new families based on it such as the the odd Burr-Hatke exponential-G family of distributions, the logarithmic\textbf{\ }Burr-Hatke exponential-G family of distributions and the generalized\textbf{\ }Burr-Hatke exponential-G family of distributions, among others.

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14

Lai, C. D., Michael B. C. Khoo, K. Muralidharan, and M. Xie. "Weibull Model Allowing Nearly Instantaneous Failures." Journal of Applied Mathematics and Decision Sciences 2007 (September 24, 2007): 1–11. http://dx.doi.org/10.1155/2007/90842.

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A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are also presented. An R script was written to fit the model parameters. An application of the modified model is illustrated.

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15

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 implemented via a straightforwardly maximum likelihood procedure. The practical importance of the new distribution was demonstrated in three applications where our distribution outperforms several former lifetime distributions, such as the exponential, the exponential-geometric, the Weibull, the modified Weibull, and the generalized exponential-Poisson distribution.

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16

Kotb, M. S. "Bayesian inference and prediction for modified Weibull distribution under generalized order statistics." Journal of Statistics and Management Systems 17, no. 5-6 (November 2, 2014): 547–78. http://dx.doi.org/10.1080/09720510.2014.903707.

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17

Ateya, Saieed F. "Estimation under modified Weibull distribution based on right censored generalized order statistics." Journal of Applied Statistics 40, no. 12 (August 5, 2013): 2720–34. http://dx.doi.org/10.1080/02664763.2013.825705.

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18

P., Jeyadurga, Usha Mahalingam, and Saminathan Balamurali. "Modified chain sampling plan for assuring percentile life under Weibull distribution and generalized exponential distribution." International Journal of Quality & Reliability Management 35, no. 9 (October 1, 2018): 1989–2005. http://dx.doi.org/10.1108/ijqrm-02-2018-0044.

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Purpose The purpose of this paper is to design a modified chain sampling plan for assuring the product percentile life where the lifetime follows Weibull or generalized exponential distributions (GEDs). In order to reduce the cost of inspection when implementing the proposed modified chain sampling plan, it is also considered the economic aspect of designing of proposed plan in this paper. Design/methodology/approach The authors have designed the proposed plan on the basis of two points on the operating characteristic (OC) curve approach. The optimization problem is used to determine the plan parameters of the proposed plan so that the specified values of producer’s risk and consumer’s risk are satisfied simultaneously. Findings The results we have obtained, confirm that the proposed plan will be very effective in reducing the sample size rather than other existing sampling plans. The OC curves of proposed plan, chain sampling plan and zero acceptance number single sampling plan show that the performance of proposed plan in discriminating the good and poor quality lots is better than other two plans. In this paper, it is proved that the value of number of preceding lots required for current lot disposition plays an important role. Originality/value The proposed modified chain sampling plan for assuring the percentile lifetime of the products under Weibull or GEDs is not available in the literature. The proposed plan can be used in all the manufacturing industries to assure the product percentile lifetime with minimum sample size as well as minimum cost.

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19

Starling, James K., Christina Mastrangelo, and Youngjun Choe. "Improving Weibull distribution estimation for generalized Type I censored data using modified SMOTE." Reliability Engineering & System Safety 211 (July 2021): 107505. http://dx.doi.org/10.1016/j.ress.2021.107505.

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20

Hüller, S., and A. Porzio. "Weibull-type speckle distributions as a result of saturation in stimulated scattering processes." Laser and Particle Beams 33, no. 4 (July 27, 2015): 667–78. http://dx.doi.org/10.1017/s0263034615000713.

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AbstractDuring the propagation of an optically smoothed laser beam through a warm plasma the speckle field pattern and the corresponding speckle intensity distribution are modified in time and along the laser propagation direction. It is shown here that the laser–plasma interaction can change the character of speckle statistics from an initially exponential-type limit law to a Weibull-type law. The Weibull distribution is characterized by a power-law-type behavior in a limited interval of the random variable, which is, in the present case, the speckle intensity. The properties of the speckle distributions are studied using methods of extremal and order statistics. The scattering instability process (here stimulated Brillouin forward scattering) causing the change in speckle statistics has an onset behavior associated with a “critical gain” value, as pointed out in work by Rose and DuBois (1993b). The saturation of the instability process as a function of intensity explains the limited interval of the Weibull-type speckle distribution. The differences in the type of the speckle statistics are analyzed by using “excess over threshold” methods relying on the generalized Pareto distribution, which clearly brings to evidence the transition from an exponential type distribution to the Weibull-type distribution as a function of the instability gain value, that is, from the regime below critical gain to values above the critical gain.

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21

Hamedani, G. G. "On Characterizations of Four Recently Introduced Distributions: Two Continuous and Two Discrete." International Journal of Statistics and Probability 8, no. 4 (June 13, 2019): 25. http://dx.doi.org/10.5539/ijsp.v8n4p25.

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Oluyede et al. (2016) and Mdlongwa et al. (2017) consider the continuous univariate distributions called Dagum-Poisson (DP) and Burr XII Modified Weibull (BXIIMW), respectively, and study certain properties and applications of these distributions. Shahid and Raheel (2019) and Para and Jan (2019) proposed the univariate discrete distributions called Discrete Modified Inverse Rayleigh (DMIR) and Discrete Generalized Inverse Weibull (DGIW) and study some of their mathematical properties. The present short note is intended to complete, in some way, the works cited above via establishing certain characterizations of these distributions in different directions.

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22

Aidi khaoula, Sanku Dey, Devendra Kumar, and Seddik-Ameur N. "Different Classical Methods of Estimation and Chi-squared Goodness-of-fit Test for Unit Generalized Inverse Weibull Distribution." Austrian Journal of Statistics 50, no. 5 (August 25, 2021): 77–100. http://dx.doi.org/10.17713/ajs.v50i5.1181.

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In this paper, we try to contribute to the distribution theory literature by incorporating a new bounded distribution, called the unit generalized inverse Weibull distribution (UGIWD) in the (0, 1) intervals by transformation method. The proposed distribution exhibits increasing and bathtub shaped hazard rate function. We derive some basic statistical properties of the new distribution. Based on complete sample, the model parameters are obtained by the methods of maximum likelihood, least square, weighted least square, percentile, maximum product of spacing and Cram`er-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap confidence intervals of the parameters of the model based on aforementioned methods of estimation are also obtained. We illustrate the performance of the proposed distribution by means of one real data set and the data set shows that the new distribution is more appropriate as compared to unit Birnbaum-Saunders, unit gamma, unit Weibull, Kumaraswamy and unit Burr III distributions. Further, we construct chi-squared goodness-of-fit tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification. The criterion test used is the modified chi-squared statistic Y^2, developedby Bagdonavi?ius and Nikulin, 2011 for some parametric models when data are censored. The performances of the proposed test are shown by an intensive simulation study and an application to real data set

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23

Goual, Hafida, and Nacira Seddik-Ameur. "A MODIFIED CHI-SQUARED GOODNESS-OF-FIT TEST FOR THE KUMARASWAMY GENERALIZED INVERSE WEIBULL DISTRIBUTION AND ITS APPLICATIONS." Journal of Statistics: Advances in Theory and Applications 16, no. 2 (December 28, 2016): 275–305. http://dx.doi.org/10.18642/jsata_7100121749.

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24

Omer, Mohamed Elamin, Mohd Abu Bakar, Mohd Adam, and Mohd Mustafa. "Utilization of a Mixture Cure Rate Model based on the Generalized Modified Weibull Distribution for the Analysis of Leukemia Patients." Asian Pacific Journal of Cancer Prevention 22, no. 4 (April 1, 2021): 1045–53. http://dx.doi.org/10.31557/apjcp.2021.22.4.1045.

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25

Martinez, Edson Z., Jorge A. Achcar, Alexandre A. A. Jácome, and José S. Santos. "Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data." Computer Methods and Programs in Biomedicine 112, no. 3 (December 2013): 343–55. http://dx.doi.org/10.1016/j.cmpb.2013.07.021.

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26

Lepikhin, A. M., N. A. Makhutov, and Yu I. Shokin. "Probabilistic multiscale modeling of fracture in heterogeneous materials and structures." Industrial laboratory. Diagnostics of materials 86, no. 7 (July 18, 2020): 45–54. http://dx.doi.org/10.26896/1028-6861-2020-86-7-45-54.

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The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

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27

Sun, Yazhen, Zhangyi Gu, Jinchang Wang, Chenze Fang, and Xuezhong Yuan. "Study on Relaxation Damage Properties of High Viscosity Asphalt Sand under Uniaxial Compression." Advances in Civil Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/1498480.

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Laboratory investigations of relaxation damage properties of high viscosity asphalt sand (HVAS) by uniaxial compression tests and modified generalized Maxwell model (GMM) to simulate viscoelastic characteristics coupling damage were carried out. A series of uniaxial compression relaxation tests were performed on HVAS specimens at different temperatures, loading rates, and constant levels of input strain. The results of the tests show that the peak point of relaxation modulus is highly influenced by the loading rate in the first half of an L-shaped curve, while the relaxation modulus is almost constant in the second half of the curve. It is suggested that for the HVAS relaxation tests, the temperature should be no less than −15°C. The GMM is used to determine the viscoelastic responses, the Weibull distribution function is used to characterize the damage of the HVAS and its evolution, and the modified GMM is a coupling of the two models. In this paper, the modified GMM is implemented through a secondary development with the USDFLD subroutine to analyze the relaxation damage process and improve the linear viscoelastic model in ABAQUS. Results show that the numerical method of coupling damage provides a better approximation of the test curve over almost the whole range. The results also show that the USDFLD subroutine can effectively predict the relaxation damage process of HVAS and can provide a theoretical support for crack control of asphalt pavements.

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28

Golub, Y. I., F. V. Starovoitov, and V. V. Starovoitov. "COMPARATIVE ANALYSIS OF NO-REFERENCE MEASURES FOR DIGITAL IMAGE SHARPNESS ASSESSMENT." Doklady BGUIR, no. 7 (125) (December 7, 2019): 113–20. http://dx.doi.org/10.35596/1729-7648-2019-125-7-113-120.

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Recently, problems of digital image sharpness determination are becoming more relevant and significant. The number of digital images used in many fields of science and technology is growing. Images obtained in various ways may have unsatisfactory quality; therefore, an important step in image processing and analysis algorithms is a quality control stage of the received data. Poor quality images can be automatically deleted. In this article we study the problem of the automatic sharpness evaluation of digital images. As a result of the scientific literature analysis, 28 functions were selected that are used to analyze the clarity of digital images by calculation local estimates. All the functions first calculate local estimates in the neighborhood of every pixel, and then use the arithmetic mean as a generalized quality index. Testing have demonstrated that many estimates of local sharpness of the image often have abnormal distribution of the data. Therefore, some modified versions of the studied functions were additionally evaluated, instead of the average of local estimates, we studied the Weibull distribution parameters (FORM, SCALE, MEAN weib, MEDIAN weib). We evaluated three variants of the correlation of quantitative sharpness assessments with the subjective assessments of human experts. Since distribution of local features is abnormal, Spearman and Kendall rank correlation coefficients were used. Correlation above 0.7 means good agreement between quantitative and visual estimates. The experiments were carried out on digital images of various quality and clarity: artificially blurred images and blurred during shooting. Summing up results of the experiments, we propose to use seven functions for automatic analysis of the digital image sharpness, which are fast calculated and better correlated with the subjective sharpness evaluation.

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29

Sewilanl, Eman M. "Generalized Weibull Distribution Revisited." المجلة العلمیة للبحوث التجاریة 14, no. 2 (October 1, 2008): 8–25. http://dx.doi.org/10.21608/sjsc.2008.118642.

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30

Mustafa, Abdelfattah, Beih S. Desouky, and Shamsan AL-Garash. "THE WEIBULL GENERALIZED FLEXIBLE WEIBULL EXTENSION DISTRIBUTION." Journal of Data Science 14, no. 3 (March 5, 2021): 453–78. http://dx.doi.org/10.6339/jds.201607_14(3).0004.

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31

Saboor, Abdus, Muhammad Nauman Khan, Gauss M. Cordeiro, Marcelino A. R. Pascoa, Juliano Bortolini, and Shahid Mubeen. "Modified beta modified-Weibull distribution." Computational Statistics 34, no. 1 (June 1, 2018): 173–99. http://dx.doi.org/10.1007/s00180-018-0822-y.

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32

Khan, Muhammad Shuaib, and Robert King. "Modified Inverse Weibull Distribution." Journal of Statistics Applications & Probability 1, no. 2 (July 1, 2012): 115–32. http://dx.doi.org/10.12785/jsap/010204.

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33

Lai, C. D., M. Xie, and D. N. P. Murthy. "A modified Weibull distribution." IEEE Transactions on Reliability 52, no. 1 (March 2003): 33–37. http://dx.doi.org/10.1109/tr.2002.805788.

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34

Khan, Muhammad Nauman, Anwaar Saeed, and Ayman Alzaatreh. "Weighted Modified Weibull Distribution." Journal of Testing and Evaluation 47, no. 5 (October 9, 2018): 20170370. http://dx.doi.org/10.1520/jte20170370.

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35

Shafaei Nooghabi, Mohamad, Gholam Reza Mohtashami Borzadaran, and Abdol Hamid Rezaei Roknabadi. "Discrete modified Weibull distribution." METRON 69, no. 2 (August 2011): 207–22. http://dx.doi.org/10.1007/bf03263557.

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36

Elbatal, I., and Hiba Z. Muhammed. "Exponentiated generalized inverse Weibull distribution." Applied Mathematical Sciences 8 (2014): 3997–4012. http://dx.doi.org/10.12988/ams.2014.44267.

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37

de Gusmão, Felipe R. S., Edwin M. M. Ortega, and Gauss M. Cordeiro. "The generalized inverse Weibull distribution." Statistical Papers 52, no. 3 (August 21, 2009): 591–619. http://dx.doi.org/10.1007/s00362-009-0271-3.

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38

Jain, Kanchan, Neetu Singla, and Suresh Kumar Sharma. "The Generalized Inverse Generalized Weibull Distribution and Its Properties." Journal of Probability 2014 (August 6, 2014): 1–11. http://dx.doi.org/10.1155/2014/736101.

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The Inverse Weibull distribution has been applied to a wide range of situations including applications in medicine, reliability, and ecology. It can also be used to describe the degradation phenomenon of mechanical components. We introduce Inverse Generalized Weibull and Generalized Inverse Generalized Weibull (GIGW) distributions. GIGW distribution is a generalization of several distributions in literature. The mathematical properties of this distribution have been studied and the mixture model of two Generalized Inverse Generalized Weibull distributions is investigated. Estimates of parameters using method of maximum likelihood have been computed through simulations for complete and censored data.

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39

Abdelall, Yassmen. "Exponentiated Transmuted Generalized Inverse Weibull Distribution a Generalization of the Generalized Inverse Weibull Distribution." Asian Research Journal of Mathematics 8, no. 2 (January 23, 2018): 1–12. http://dx.doi.org/10.9734/arjom/2018/38369.

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40

Ahmad, Zubair, and Zawar Hussain. "Modified New Flexible Weibull Distribution." Circulation in Computer Science 2, no. 6 (July 20, 2017): 7–13. http://dx.doi.org/10.22632/ccs-2017-252-30.

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The present paper is devoted to introduce a four-parameter modification of new flexible Weibull distribution. The proposed model will be called modified new flexible Weibull distribution, able to model lifetime phenomena with increasing or bathtub-shaped failure rates. Some of its mathematical properties will be studied. The approach of maximum likelihood will be used for estimating the model parameters. A brief mathematical description for the reliability function will also be discussed. The usefulness of the proposed distribution will be illustrated by an application to a real data set.

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41

Khan, Muhammad Nauman. "The Modified Beta Weibull Distribution." Hacettepe Journal of Mathematics and Statistics 45, no. 40 (November 23, 2014): 1. http://dx.doi.org/10.15672/hjms.2014408152.

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42

Shahen, H. S., A. H. El-Bassiouny, and Mohamed Abouhawwash. "Bivariate Exponentiated Modified Weibull Distribution." Journal of Statistics Applications & Probability 8, no. 1 (March 1, 2019): 27–39. http://dx.doi.org/10.18576/jsap/080103.

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43

VARDHAN, R. Vishnu, and S. BALASWAMY. "Transmuted New Modified Weibull Distribution." Mathematical Sciences and Applications E-Notes 4, no. 1 (April 15, 2016): 125–35. http://dx.doi.org/10.36753/mathenot.421421.

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44

Sarhan, Ammar M., and Joseph Apaloo. "Exponentiated modified Weibull extension distribution." Reliability Engineering & System Safety 112 (April 2013): 137–44. http://dx.doi.org/10.1016/j.ress.2012.10.013.

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45

Almalki, Saad J., and Jingsong Yuan. "A new modified Weibull distribution." Reliability Engineering & System Safety 111 (March 2013): 164–70. http://dx.doi.org/10.1016/j.ress.2012.10.018.

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46

He, Bo, Weimin Cui, and Xiaofeng Du. "An additive modified Weibull distribution." Reliability Engineering & System Safety 145 (January 2016): 28–37. http://dx.doi.org/10.1016/j.ress.2015.08.010.

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47

Wang, Min, and Ibrahim Elbatal. "The modified Weibull geometric distribution." METRON 73, no. 3 (August 15, 2014): 303–15. http://dx.doi.org/10.1007/s40300-014-0052-1.

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48

Silva, Giovana O., Edwin M. M. Ortega, and Gauss M. Cordeiro. "The beta modified Weibull distribution." Lifetime Data Analysis 16, no. 3 (March 18, 2010): 409–30. http://dx.doi.org/10.1007/s10985-010-9161-1.

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49

Muhammad, Sabah, and Kareema Abed AL-Kadim. "Odd Generalized Exponential Weibull Exponential Distribution." Journal of Engineering and Applied Sciences 14, no. 8 (November 30, 2019): 10360–68. http://dx.doi.org/10.36478/jeasci.2019.10360.10368.

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50

Khan, Muhammad Shuaib, Robert King, and Irene Lena Hudson. "Transmuted New Generalized Inverse Weibull Distribution." Pakistan Journal of Statistics and Operation Research 13, no. 2 (June 1, 2017): 277. http://dx.doi.org/10.18187/pjsor.v13i2.1523.

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