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Journal articles on the topic 'Mixture of Kumaraswamy distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Rocha, Ricardo, Saralees Nadarajah, Vera Tomazella, Francisco Louzada, and Amanda Eudes. "New defective models based on the Kumaraswamy family of distributions with application to cancer data sets." Statistical Methods in Medical Research 26, no. 4 (June 19, 2015): 1737–55. http://dx.doi.org/10.1177/0962280215587976.

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An alternative to the standard mixture model is proposed for modeling data containing cured elements or a cure fraction. This approach is based on the use of defective distributions to estimate the cure fraction as a function of the estimated parameters. In the literature there are just two of these distributions: the Gompertz and the inverse Gaussian. Here, we propose two new defective distributions: the Kumaraswamy Gompertz and Kumaraswamy inverse Gaussian distributions, extensions of the Gompertz and inverse Gaussian distributions under the Kumaraswamy family of distributions. We show in fact that if a distribution is defective, then its extension under the Kumaraswamy family is defective too. We consider maximum likelihood estimation of the extensions and check its finite sample performance. We use three real cancer data sets to show that the new defective distributions offer better fits than baseline distributions.

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2

Ghosh, Indranil. "A NEW CLASS OF KUMARASWAMY MIXTURE DISTRIBUTION FOR INCOME MODELING." Far East Journal of Theoretical Statistics 51, no. 3 (February 11, 2016): 129–51. http://dx.doi.org/10.17654/fjtsnov2015_129_151.

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3

Noor, Farzana, Saadia Masood, Mehwish Zaman, Maryam Siddiqa, Raja Asif Wagan, Imran Ullah Khan, and Ahthasham Sajid. "Bayesian Analysis of Inverted Kumaraswamy Mixture Model with Application to Burning Velocity of Chemicals." Mathematical Problems in Engineering 2021 (May 18, 2021): 1–18. http://dx.doi.org/10.1155/2021/5569652.

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Burning velocity of different chemicals is estimated using a model from mixed population considering inverted Kumaraswamy (IKum) distribution for component parts. Two estimation techniques maximum likelihood estimation (MLE) and Bayesian analysis are applied for estimation purposes. BEs of a mixture model are obtained using gamma, inverse beta prior, and uniform prior distribution with two loss functions. Hyperparameters are determined through the empirical Bayesian method. An extensive simulation study is also a part of the study which is used to foresee the characteristics of the presented model. Application of the IKum mixture model is presented through a real dataset. We observed from the results that Linex loss performed better than squared error loss as it resulted in lower risks. And similarly gamma prior is preferred over other priors.

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4

ZeinEldin, Ramadan A., Farrukh Jamal, Christophe Chesneau, and Mohammed Elgarhy. "Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications." Symmetry 11, no. 12 (November 28, 2019): 1459. http://dx.doi.org/10.3390/sym11121459.

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In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics.

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5

Adham, Samia A., and Anfal A. ALgfary. "Bayesian estimation and prediction for a mixture of exponentiated Kumaraswamy distributions." International Journal of Contemporary Mathematical Sciences 11 (2016): 497–508. http://dx.doi.org/10.12988/ijcms.2016.61165.

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6

Lawal, Bayo H. "On Some Mixture Models for Over-dispersed Binary Data." International Journal of Statistics and Probability 6, no. 2 (February 27, 2017): 134. http://dx.doi.org/10.5539/ijsp.v6n2p134.

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In this paper, we consider several binomial mixture models for fitting over-dispersed binary data. The models range from the binomial itself, to the beta-binomial (BB), the Kumaraswamy distributions I and II (KPI \& KPII) as well as the McDonald generalized beta-binomial mixed model (McGBB). The models are applied to five data sets that have received attention in various literature. Because of convergence issues, several optimization methods ranging from the Newton-Raphson to the quasi-Newton optimization algorithms were employed with SAS PROC NLMIXED using the Adaptive Gaussian Quadrature as the integral approximation method within PROC NLMIXED. Our results differ from those presented in Li, Huang and Zhao (2011) for the example data sets in that paper but agree with those presented in Manoj, Wijekoon and Yapa (2013). We also applied these models to the case where we have a $k$ vector of covariates $(x_1, x_2, \ldots, x_k)^{'}$. Our results here suggest that the McGBB performs better than the other models in the GLM framework. All computations in this paper employed PROC NLMIXED in SAS. We present in the appendix a sample of the SAS program employed for implementing the McGBB model for one of the examples.

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7

Shuaib Khan, Muhammad, Robert King, and Irene Lena Hudson. "TRANSMUTED KUMARASWAMY DISTRIBUTION." Statistics in Transition. New Series 17, no. 2 (2016): 183–210. http://dx.doi.org/10.21307/stattrans-2016-013.

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8

Ahmed, Mohamed Ali, Mahmoud Riad Mahmoud, and Elsayed Ahmed ElSherpieny. "The New Kumaraswamy Kumaraswamy Weibull Distribution with Application." Pakistan Journal of Statistics and Operation Research 12, no. 1 (March 2, 2016): 165. http://dx.doi.org/10.18187/pjsor.v12i1.1129.

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9

Nassar, Manal Mohamed. "The Kumaraswamy Laplace Distribution." Pakistan Journal of Statistics and Operation Research 12, no. 4 (December 1, 2016): 609. http://dx.doi.org/10.18187/pjsor.v12i4.1485.

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10

Bourguignon, Marcelo, Rodrigo B. Silva, Luz M. Zea, and Gauss M. Cordeiro. "The Kumaraswamy Pareto distribution." Journal of Statistical Theory and Applications 12, no. 2 (2013): 129. http://dx.doi.org/10.2991/jsta.2013.12.2.1.

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11

George, Roshini, and S. Thobias. "Marshall-Olkin Kumaraswamy distribution." International Mathematical Forum 12 (2017): 47–69. http://dx.doi.org/10.12988/imf.2017.611151.

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12

Eljabri, S., and S. Nadarajah. "The Kumaraswamy GEV distribution." Communications in Statistics - Theory and Methods 46, no. 20 (October 4, 2016): 10203–35. http://dx.doi.org/10.1080/03610926.2016.1231815.

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13

Cordeiro, Gauss M., Saralees Nadarajah, and Edwin M. M. Ortega. "The Kumaraswamy Gumbel distribution." Statistical Methods & Applications 21, no. 2 (November 15, 2011): 139–68. http://dx.doi.org/10.1007/s10260-011-0183-y.

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14

Silva, Raquel C. da, Jeniffer J. D. Sanchez, Fábio P. Lima, and Gauss M. Cordeiro. "The Kumaraswamy Gompertz Distribution." Journal of Data Science 13, no. 2 (April 8, 2021): 241–60. http://dx.doi.org/10.6339/jds.201504_13(2).0002.

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15

Shahbaz, Muhammad Qaiser, Saman Shahbaz, and Nadeem Shafique Butt. "The Kumaraswamy–Inverse Weibull Distribution." Pakistan Journal of Statistics and Operation Research 8, no. 3 (July 1, 2012): 479. http://dx.doi.org/10.18187/pjsor.v8i3.520.

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16

Abdul-Moniem, Ibrahim B. "The Kumaraswamy Power Function Distribution." Journal of Statistics Applications & Probability 6, no. 1 (March 1, 2017): 81–90. http://dx.doi.org/10.18576/jsap/060107.

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17

Mameli, Valentina. "The Kumaraswamy skew-normal distribution." Statistics & Probability Letters 104 (September 2015): 75–81. http://dx.doi.org/10.1016/j.spl.2015.04.031.

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18

Kozubowski, Tomasz J., and Krzysztof Podgórski. "Kumaraswamy Distribution and Random Extrema." Open Statistics & Probability Journal 9, no. 1 (July 31, 2018): 18–25. http://dx.doi.org/10.2174/1876527001809010017.

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Objective:We provide a new stochastic representation for a Kumaraswamy random variable with arbitrary non-negative parameters. The representation is in terms of maxima and minima of independent distributed standard uniform components and extends a similar representation for integer-valued parameters.Result:The result is further extended for generalized classes of distributions obtained from a “base” distribution functionFviz.G(x) =H(F(x)), whereHis the CDF of Kumaraswamy distribution.

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19

Rodrigues, Jailson, and Ana Silva. "The Exponentiated Kumaraswamy-Exponential Distribution." British Journal of Applied Science & Technology 10, no. 5 (January 10, 2015): 1–12. http://dx.doi.org/10.9734/bjast/2015/16935.

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20

Saulo, Helton, Jeremias Leão, and Marcelo Bourguignon. "The Kumaraswamy Birnbaum–Saunders Distribution." Journal of Statistical Theory and Practice 6, no. 4 (December 2012): 745–59. http://dx.doi.org/10.1080/15598608.2012.719814.

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21

Elbatal, I. "The Kumaraswamy Exponentiated Pareto Distribution." Economic Quality Control 28, no. 1 (January 1, 2013): 1–8. http://dx.doi.org/10.1515/eqc-2013-0006.

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22

George, Roshini, and S. Thobias. "Kumaraswamy Marshall-Olkin Exponential distribution." Communications in Statistics - Theory and Methods 48, no. 8 (March 8, 2018): 1920–37. http://dx.doi.org/10.1080/03610926.2018.1440594.

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23

Wang, Bing Xing, Xiu Kun Wang, and Keming Yu. "Inference on the Kumaraswamy distribution." Communications in Statistics - Theory and Methods 46, no. 5 (March 17, 2016): 2079–90. http://dx.doi.org/10.1080/03610926.2015.1032425.

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24

Nadarajah, Saralees. "On the distribution of Kumaraswamy." Journal of Hydrology 348, no. 3-4 (January 2008): 568–69. http://dx.doi.org/10.1016/j.jhydrol.2007.09.008.

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25

Tahir, Muhammad Hussain, Gauss M. Cordeiro, Muhammad Mansoor, Muhammad Zubair, and Ayman Alzaatreh. "The Kumaraswamy Pareto IV Distribution." Austrian Journal of Statistics 50, no. 5 (August 25, 2021): 1–22. http://dx.doi.org/10.17713/ajs.v50i5.96.

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We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.

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26

Garg, Mridula. "On Distribution of Order Statistics from Kumaraswamy Distribution." Kyungpook mathematical journal 48, no. 3 (September 30, 2008): 411–17. http://dx.doi.org/10.5666/kmj.2008.48.3.411.

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27

Nofal, Zohdy M., Ahmed Z. Afify, Haitham M. Yousof, Daniele C. T. Granzotto, and Francisco Louzada. "Kumaraswamy Transmuted Exponentiated Additive Weibull Distribution." International Journal of Statistics and Probability 5, no. 2 (February 22, 2016): 78. http://dx.doi.org/10.5539/ijsp.v5n2p78.

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This paper introduces a new lifetime model which is a generalization of the transmuted exponentiated additive Weibull distribution by using the Kumaraswamy generalized (Kw-G) distribution. With the particular case no less than \textbf{seventy nine} sub models as special cases, the so-called Kumaraswamy transmuted exponentiated additive Weibull distribution, introduced by Cordeiro and de Castro (2011) is one of this particular cases. Further, expressions for several probabilistic measures are provided, such as probability density function, hazard function, moments, quantile function, mean, variance and median, moment generation function, R\'{e}nyi and q entropies, order estatistics, etc. Inference is maximum likelihood based and the usefulness of the model is showed by using a real dataset.

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28

Carrasco, Jalmar M. F., and Gauss M. Cordeiro. "An Extension of the Kumaraswamy Distribution." International Journal of Statistics and Probability 6, no. 3 (May 14, 2017): 61. http://dx.doi.org/10.5539/ijsp.v6n3p61.

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We propose and study a new five-parameter continuous distribution in the unit interval through a specific probability integral transform. The new distribution, under some parameter constraints, is an identified parametric model that includes as special cases six important models such as the Kumaraswamy and beta distributions. We obtain ordinary and incomplete moments, quantile and generating functions, mean deviations, R\'enyi entropy and moments of order statistics. The estimation of the model parameters is performed by maximum likelihood, and hypothesis tests are discussed. Additionally, through a simulation study we investigate the behavior of the maximum likelihood estimator, also we investigate the impact of ignoring identifiability problems. The usefulness of the proposed distribution is illustrated by means of a real data set.

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29

Reheem, Hanaa Abdel Salem, and Mona Nazih Abdel Bary. "ESTIMATION PARAMETERS OF KUMARASWAMY PRANAV DISTRIBUTION." JP Journal of Biostatistics 16, no. 2 (July 10, 2019): 47–56. http://dx.doi.org/10.17654/bs016020047.

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30

Bursa, Nurbanu, and Gamze Ozel. "The exponentiated Kumaraswamy-power function distribution." Hacettepe Journal of Mathematics and Statistics 46, no. 2 (January 6, 2017): 1–19. http://dx.doi.org/10.15672/hjms.2017.411.

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31

Elgarhy, M., Vikas Kumar Sharma, and I. Elbatal. "Transmuted Kumaraswamy Lindley distribution with application." Journal of Statistics and Management Systems 21, no. 6 (September 24, 2018): 1083–104. http://dx.doi.org/10.1080/09720510.2018.1481003.

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32

K.A, Adepoju,, Chukwu, A.U, and Shittu, O.I. "On the Kumaraswamy Fisher Snedecor Distribution." Mathematics and Statistics 4, no. 1 (February 2016): 1–14. http://dx.doi.org/10.13189/ms.2016.040101.

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33

Mitnik, Pablo A. "New Properties of the Kumaraswamy Distribution." Communications in Statistics - Theory and Methods 42, no. 5 (March 2013): 741–55. http://dx.doi.org/10.1080/03610926.2011.581782.

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34

Dey, Sanku, Josmar Mazucheli, and Saralees Nadarajah. "Kumaraswamy distribution: different methods of estimation." Computational and Applied Mathematics 37, no. 2 (March 29, 2017): 2094–111. http://dx.doi.org/10.1007/s40314-017-0441-1.

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35

Elgarhy, M., Muhammad Ahsan ul Haq, and Qurat ul Ain. "Exponentiated Generalized Kumaraswamy Distribution with Applications." Annals of Data Science 5, no. 2 (August 17, 2017): 273–92. http://dx.doi.org/10.1007/s40745-017-0128-x.

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36

ZeinEldin, Ramadan A., Christophe Chesneau, Farrukh Jamal, and Mohammed Elgarhy. "Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution." Mathematics 7, no. 10 (October 22, 2019): 1002. http://dx.doi.org/10.3390/math7101002.

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In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.

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37

Ghosh, Indranil, and G. G. Hamedani. "The Gamma–Kumaraswamy distribution: An alternative to Gamma distribution." Communications in Statistics - Theory and Methods 47, no. 9 (February 2, 2018): 2056–72. http://dx.doi.org/10.1080/03610926.2015.1122055.

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38

Iqbal, Zafar, Muhammad Maqsood Tahir, Naureen Riaz, Syed Azeem Ali, and Munir Ahmad. "Generalized Inverted Kumaraswamy Distribution: Properties and Application." Open Journal of Statistics 07, no. 04 (2017): 645–62. http://dx.doi.org/10.4236/ojs.2017.74045.

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39

Rasekhi, Mahdi, Morad Alizadeh, and G. G. Hamedani. "The Kumaraswamy Weibull Geometric Distribution with Applications." Pakistan Journal of Statistics and Operation Research 14, no. 2 (June 1, 2018): 347. http://dx.doi.org/10.18187/pjsor.v14i2.1551.

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40

Usman, Rana Muhammad, Muhammad Ahsan ul Haq, and Junaid Talib. "Kumaraswamy Half-Logistic Distribution: Properties and Applications." Journal of Statistics Applications & Probability 6, no. 3 (November 1, 2017): 597–609. http://dx.doi.org/10.18576/jsap/060315.

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41

Rashwan, Nasr Ibrahim. "A Note on Kumaraswamy Exponentiated Rayleigh distribution." Journal of Statistical Theory and Applications 15, no. 3 (2016): 286. http://dx.doi.org/10.2991/jsta.2016.15.3.8.

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42

de Gusmão, Felipe R. S., Vera L. D. Tomazella, and Ricardo S. Ehlers. "Bayesian Estimation of the Kumaraswamy InverseWeibull Distribution." Journal of Statistical Theory and Applications 16, no. 2 (2017): 248. http://dx.doi.org/10.2991/jsta.2017.16.2.9.

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43

Al-saiary, Zakeia A., Rana A. Bakoban, and Areej A. Al-zahrani. "Characterizations of the Beta Kumaraswamy Exponential Distribution." Mathematics 8, no. 1 (December 20, 2019): 23. http://dx.doi.org/10.3390/math8010023.

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In this article, the five-parameter beta Kumaraswamy exponential distribution (BKw-E) is introduced, and some characterizations of this distribution are obtained. The shape of the hazard function and some other important properties—such as median, mode, quantile function, and mean—are studied. In addition, the moments, skewness, and kurtosis are found. Furthermore, important measures such as Rényi entropy and order statistics are obtained; these have applications in many fields. An example of a real data set is discussed.

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44

Bakouch, Hassan S., Fernando A. Moala, Abdus Saboor, and Haniya Samad. "A bivariate Kumaraswamy-exponential distribution with application." Mathematica Slovaca 69, no. 5 (October 25, 2019): 1185–212. http://dx.doi.org/10.1515/ms-2017-0300.

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Abstract In this paper, we introduce a new bivariate Kumaraswamy exponential distribution, whose marginals are univariate Kumaraswamy exponential. Some probabilistic properties of this bivariate distribution are derived, such as joint density function, marginal density functions, conditional density functions, moments and stress-strength reliability. Also, we provide the expected information matrix with its elements in a closed form. Estimation of the parameters is investigated by the maximum likelihood, Bayesian and least squares estimation methods. A simulation study is carried out to compare the performance of the estimators by estimation methods. Further, one data set have been analyzed to show how the proposed distribution works in practice.

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45

Muhammed, Hiba Z. "On a bivariate generalized inverted Kumaraswamy distribution." Physica A: Statistical Mechanics and its Applications 553 (September 2020): 124281. http://dx.doi.org/10.1016/j.physa.2020.124281.

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46

Mohammed, H. F. "Inference on the log-exponentiated Kumaraswamy distribution." International Journal of Contemporary Mathematical Sciences 12 (2017): 165–79. http://dx.doi.org/10.12988/ijcms.2017.7417.

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47

Aly, Hanan M., and Ola A. Abuelamayem. "Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation." Mathematical Problems in Engineering 2020 (October 21, 2020): 1–27. http://dx.doi.org/10.1155/2020/6349523.

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Industrial revolution leads to the manufacturing of multicomponent products; to guarantee the sufficiency of the product and consumer satisfaction, the producer has to study the lifetime of the products. This leads to the use of bivariate and multivariate lifetime distributions in reliability engineering. The most popular and applicable is Marshall–Olkin family of distributions. In this paper, a new bivariate lifetime distribution which is the bivariate inverted Kumaraswamy (BIK) distribution is found and its properties are illustrated. Estimation using both maximum likelihood and Bayesian approaches is accomplished. Using different selection criteria, it is found that BIK provides the best performance compared with other bivariate distributions like bivariate exponential and bivariate inverse Weibull distributions. As a generalization, the multivariate inverted Kumaraswamy (MIK) distribution is derived. Few studies have been conducted on the multivariate Marshall–Olkin lifetime distributions. To the best of our knowledge, none of them handle estimation process. In this paper, we developed an algorithm to show how to estimate the unknown parameters of MIK using both maximum likelihood and Bayesian approaches. This algorithm could be applied in estimating other Marshall–Olkin multivariate lifetime distributions.

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48

Lemonte, Artur J. "Improved point estimation for the Kumaraswamy distribution." Journal of Statistical Computation and Simulation 81, no. 12 (December 2011): 1971–82. http://dx.doi.org/10.1080/00949655.2010.511621.

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49

Nadarajah, Saralees, Gauss M. Cordeiro, and Edwin M. M. Ortega. "General results for the Kumaraswamy-G distribution." Journal of Statistical Computation and Simulation 82, no. 7 (July 2012): 951–79. http://dx.doi.org/10.1080/00949655.2011.562504.

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50

Mirhosseini, S. M., A. Dolati, and M. Amini. "On a bivariate Kumaraswamy type exponential distribution." Communications in Statistics - Theory and Methods 45, no. 18 (December 18, 2015): 5461–77. http://dx.doi.org/10.1080/03610926.2014.944664.

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