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A New Extension Form for Continuous Probability Distributions: Uniform-X Distributions

Year 2022, , 351 - 357, 29.06.2022

Çiğdem Topçu Gülöksüz , Nuri Çelik

https://doi.org/10.17776/csj.1037935

Abstract

In this paper, generating extension forms for continuous probability distribution functions is studied. The considered transformer function is applied to three well-known probability distributions- Normal, Kumaraswamy, Weibull- and new extensions of these distributions are obtained. The related functions of the new extensions are defined, random samples are generated from the new extensions and the results are presented. Parameter estimation procedures of the extensions are studied, and likelihood equations are obtained. To demonstrate the modeling performance of the extensions, three different data sets are considered, separately. Each data set is modeled by both the corresponding probability distribution and its extensions. The new extensions give the best fit to the corresponding data over the well-known probability distributions. 

Keywords

Extensions of probability distributions Transformer function Quantile function Maximum likelihood estimation Skewness.

References

  • [1] Amoroso L.R., Intorno Alla Curva dei Redditi, Annali de Mathematica Series, 4 (2) (1925) 123-159.
  • [2] Good I.J. The Population Frequencies of the Species and the Estimation of Population Parameters, Biometrika, 40 (1953) 237-260.
  • [3] Hoskings J.R.M., Wallis J.R. Parameter and Quantile Estimation for the Generalized Pareto Distribution, Technometrics, 29 (1987) 339-349.
  • [4] Kınacı İ., Kuş C., Karakaya, K. and Akdoğan Y. APT-Pareto Distribution and its Properties, Cumhuriyet Science Journal, 40 (2) (2019) 378-387.
  • [5] Ljubo M. Curves and Concentration Indices Generalized Pareto Distributions, Statistical Review, 15 (1965) 257-260.
  • [6] McDonald J.B., Some Generalized Functions for the Size Distribution of Income, Econometrica, 52 (1984) 647-663.
  • [7] Eugene E., Lee C., Famoye F., The beta-normal distribution and its application, Commun.Stat, Theory Methods, 31 (4) (2002) 497-512.
  • [8] Akinsete A., Famoye F., Lee C. The beta-Pareto distribution, Statistics, 42 (2008) 457-563.
  • [9] Alshawarbeh E., Famoye F., Lee C. The beta-Cauchy distribution: some properties and applications, Journal of Statistical Theory and Applications, 12 (4) (2013) 378-391.
  • [10] Barreto-Souza W., Santos A.H.S., Corderio G.M., The beta generalized exponential distribution, Journal of Statistical Computation and Simulation, 80 (2) (2010) 159-172.
  • [11] Famoye F., Lee C., Olumolade O., The beta-Weibull distribution, J. Stat. Theory Appl., 4 (2) (2005) 121-136.
  • [12] Nadarajah S., Kotz S., The beta Gumbel distribution, Math. Probl. Eng., 4 (2004) 323-332.
  • [13] Nadarajah S., Kotz S., The beta exponential distribution, Reliab. Eng. Syst. Saf., 91 (6) (2005) 689-697.
  • [14] Jones M.C., Kumaraswamys distribution: a beta type distribution with tractability advantages, Stat. Methodology, 6 (2008) 70-81.
  • [15] Cordeiro G.M., Ortega E.M.M., Nadarajah S., The Kumaraswamy Weibull distribution with application to failure data, J. Franklin Inst., 347 (2010) 399-429.
  • [16] Cordeiro G.M., Pescim R.R., Ortega E.M.M., The Kumaraswamy generalized half-normal distribution for skewed positive data, J. Data Sci., 10 (2012) 195-224.
  • [17] de Castro M.A.R., Ortega E.M.M., Cordeiro G.M., The Kumaraswamy generalized gamma distribution with application in survival analysis, Stat. Methodol, 8 (5) (2011) 411-433.
  • [18] Alzaatreh A., Lee C., Famoye F. A new method for generating families of continuous distributions, Metron, 71 (2013) 63-79.
  • [19] Celik N., Guloksuz CT., A new lifetime distribution, EksploatacjaI Niezawodnosc (Maintenance and Reliability), 19 (4) (2017) 634-639.
  • [20] Guloksuz CT., Celik N., An Extension of Generalized Extreme Value Distribution: Uniform-GEV Distribution and Its Application to Earthquake Data, Thailand Statistician, 18 (4) (2020) 491-506.
  • [21] Celik N., Robust Statistical Inference in ANOVA Models Using Skew Distributions and Applications”, Phd Thesis, Ankara University, Graduate School of Natural and Applied Sciences, Turkey, 2012.
  • [22] Meeker W.Q., Escobar L.A., Statistical methods for reliability data. USA: Wiley Series, (1998)
  • [23] Javanshiri Z., Habibi Rad A., Arghami N.R. Exp-Kumaraswamy Distributions: Some Properties and Applications, Journal of Sciences, Islamic Republic of Iran, 26 (1) (2015) 57-69.

Year 2022, , 351 - 357, 29.06.2022

Çiğdem Topçu Gülöksüz , Nuri Çelik

https://doi.org/10.17776/csj.1037935

Abstract

References

  • [1] Amoroso L.R., Intorno Alla Curva dei Redditi, Annali de Mathematica Series, 4 (2) (1925) 123-159.
  • [2] Good I.J. The Population Frequencies of the Species and the Estimation of Population Parameters, Biometrika, 40 (1953) 237-260.
  • [3] Hoskings J.R.M., Wallis J.R. Parameter and Quantile Estimation for the Generalized Pareto Distribution, Technometrics, 29 (1987) 339-349.
  • [4] Kınacı İ., Kuş C., Karakaya, K. and Akdoğan Y. APT-Pareto Distribution and its Properties, Cumhuriyet Science Journal, 40 (2) (2019) 378-387.
  • [5] Ljubo M. Curves and Concentration Indices Generalized Pareto Distributions, Statistical Review, 15 (1965) 257-260.
  • [6] McDonald J.B., Some Generalized Functions for the Size Distribution of Income, Econometrica, 52 (1984) 647-663.
  • [7] Eugene E., Lee C., Famoye F., The beta-normal distribution and its application, Commun.Stat, Theory Methods, 31 (4) (2002) 497-512.
  • [8] Akinsete A., Famoye F., Lee C. The beta-Pareto distribution, Statistics, 42 (2008) 457-563.
  • [9] Alshawarbeh E., Famoye F., Lee C. The beta-Cauchy distribution: some properties and applications, Journal of Statistical Theory and Applications, 12 (4) (2013) 378-391.
  • [10] Barreto-Souza W., Santos A.H.S., Corderio G.M., The beta generalized exponential distribution, Journal of Statistical Computation and Simulation, 80 (2) (2010) 159-172.
  • [11] Famoye F., Lee C., Olumolade O., The beta-Weibull distribution, J. Stat. Theory Appl., 4 (2) (2005) 121-136.
  • [12] Nadarajah S., Kotz S., The beta Gumbel distribution, Math. Probl. Eng., 4 (2004) 323-332.
  • [13] Nadarajah S., Kotz S., The beta exponential distribution, Reliab. Eng. Syst. Saf., 91 (6) (2005) 689-697.
  • [14] Jones M.C., Kumaraswamys distribution: a beta type distribution with tractability advantages, Stat. Methodology, 6 (2008) 70-81.
  • [15] Cordeiro G.M., Ortega E.M.M., Nadarajah S., The Kumaraswamy Weibull distribution with application to failure data, J. Franklin Inst., 347 (2010) 399-429.
  • [16] Cordeiro G.M., Pescim R.R., Ortega E.M.M., The Kumaraswamy generalized half-normal distribution for skewed positive data, J. Data Sci., 10 (2012) 195-224.
  • [17] de Castro M.A.R., Ortega E.M.M., Cordeiro G.M., The Kumaraswamy generalized gamma distribution with application in survival analysis, Stat. Methodol, 8 (5) (2011) 411-433.
  • [18] Alzaatreh A., Lee C., Famoye F. A new method for generating families of continuous distributions, Metron, 71 (2013) 63-79.
  • [19] Celik N., Guloksuz CT., A new lifetime distribution, EksploatacjaI Niezawodnosc (Maintenance and Reliability), 19 (4) (2017) 634-639.
  • [20] Guloksuz CT., Celik N., An Extension of Generalized Extreme Value Distribution: Uniform-GEV Distribution and Its Application to Earthquake Data, Thailand Statistician, 18 (4) (2020) 491-506.
  • [21] Celik N., Robust Statistical Inference in ANOVA Models Using Skew Distributions and Applications”, Phd Thesis, Ankara University, Graduate School of Natural and Applied Sciences, Turkey, 2012.
  • [22] Meeker W.Q., Escobar L.A., Statistical methods for reliability data. USA: Wiley Series, (1998)
  • [23] Javanshiri Z., Habibi Rad A., Arghami N.R. Exp-Kumaraswamy Distributions: Some Properties and Applications, Journal of Sciences, Islamic Republic of Iran, 26 (1) (2015) 57-69.
There are 23 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Çiğdem Topçu Gülöksüz 0000-0002-7433-1297

Nuri Çelik 0000-0002-4234-2389

Publication Date June 29, 2022
Submission Date December 17, 2021
Acceptance Date April 28, 2022
Published in Issue Year 2022

Cite

APA Topçu Gülöksüz, Ç., & Çelik, N. (2022). A New Extension Form for Continuous Probability Distributions: Uniform-X Distributions. Cumhuriyet Science Journal, 43(2), 351-357. https://doi.org/10.17776/csj.1037935