Arctan exponential extension distribution with properties and applications

In the presented work, a continuous distribution named arctan exponential extension distribution has been introduced along with relevant properties which are statistically and mathematically derived and analyzed. While estimating the model parameters, three well-known estimation methods are employed which are Cramer-Von-Mises (CVM), maximum likelihood estimation (MLE) and least-square estimation (LSE) methods. With the help of a real set of data, in comparison to existing models, the presented distribution’s goodness-of-fit is evaluated.

[1]  H. Bolfarine,et al.  A New Extension of the Exponential Distribution , 2014 .

[2]  Gauss M. Cordeiro,et al.  A new family of generalized distributions , 2011 .

[3]  N. Balakrishnan,et al.  The gamma-exponentiated exponential distribution , 2012 .

[4]  Artur J. Lemonte.  A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function , 2013, Comput. Stat. Data Anal..

[5]  J. J. Swain,et al.  Least-squares estimation of distribution functions in johnson's translation system , 1988 .

[6]  A. M. Abouammoh,et al.  Reliability estimation of generalized inverted exponential distribution , 2009 .

[7]  Debasis Kundu,et al.  Generalized Rayleigh distribution: different methods of estimations , 2005, Comput. Stat. Data Anal..

[8]  J. Moors,et al.  A quantile alternative for kurtosis , 1988 .

[9]  Saralees Nadarajah,et al.  An extension of the exponential distribution , 2011 .

[10]  Debasis Kundu,et al.  A new method for generating distributions with an application to exponential distribution , 2017 .

[11]  Saralees Nadarajah,et al.  A new lifetime distribution , 2014 .

[12]  Gauss M. Cordeiro,et al.  The beta generalized exponential distribution , 2008, 0809.1889.

[13]  Half Logistic Exponential Extension Distribution with Properties and Applications , 2020 .

[14]  A. Hassan,et al.  Alpha power transformed extended exponential distribution: properties and applications , 2018, Journal of Nonlinear Sciences and Applications.

[15]  E. Calderín-Ojeda,et al.  MODELLING INSURANCE DATA WITH THE PARETO ARCTAN DISTRIBUTION , 2015, ASTIN Bulletin.

[16]  Thomas Mailund.  Functional Programming in R: Advanced Statistical Programming for Data Science, Analysis and Finance , 2017 .

[17]  Faton Merovci,et al.  Transmuted Rayleigh Distribution , 2016 .

[18]  Ahmad M. Alshamrani,et al.  The generalized Gompertz distribution , 2013 .

[19]  Truncated Cauchy Power–Exponential Distribution with Theory and Applications , 2020 .

[20]  A new extension of exponential distribution with statistical properties and applications , 2018, Journal of Nonlinear Sciences and Applications.

[21]  Debasis Kundu,et al.  Generalized exponential distribution: Existing results and some recent developments , 2007 .

[22]  Samuel Kotz,et al.  The beta exponential distribution , 2006, Reliab. Eng. Syst. Saf..

[23]  Hilary I. Okagbue,et al.  The Weibull-Exponential Distribution: Its Properties and Applications , 2015 .

[24]  Lee J. Bain,et al.  An exponential power life-testing distribution , 1975 .