Abstract
In this study, an alpha power inverted Kumaraswamy (APIK) distribution is introduced. The APIK distribution is de- rived by applying alpha power transformation to an inverted Kumaraswamy distribution. Some submodels and limiting cases of the APIK distribution are obtained as well. To the best of the authors’ knowledge, some of these distributions have not been introduced yet. Statistical inference of the APIK distribution, including survival and hazard rate func- tions, are obtained. Unknown parameters of the APIK distribution are estimated by using the maximum likelihood (ML), maximum product of spacings (MPS), and least squares (LS) methods. A Monte Carlo simulation study is con- ducted to compare the efficiencies of the ML estimators of the shape parameters α, β and λ of the APIK distribution with their MPS and LS counterparts. An application to a real data set is provided to show the implementation and modeling capability of the APIK distribution.
Highlights
Probability distribution functions are usually used for modeling data from various fields
This study presents the following contributions to the related literature. (i) An alpha power inverted Kumaraswamy (APIK) distribution is introduced as an alternative to the IKum and some of its extended/generalized versions such as the Marshall-Olkin extended inverted Kumaraswamy (MOEIK) and generalized inverted Kumaraswamy (GIKw)-W distributions. (ii) Several submodels and limiting cases of the APIK distribution, to the best of the Authors’ knowledge, some of them have not been proposed yet, are obtained as well. (iii) The maximum likelihood (ML), maximum product of spacings (MPS) and least squares (LS) methods are used to estimate the unknown parameters of the APIK distribution
Modeling performances of the IKum, APIK, MOEIK, and GIKw-W distributions are compared by using well-known information criteria such as value of the ln L, Akaike Information Criterion (AIC), corrected AIC (AICc), and goodness-of-fit measures the Kolmogorov-Smirnov (KS), root-mean-squared error (RMSE) and coefficent of determination (R2)
Summary
Probability distribution functions are usually used for modeling data from various fields. Bagci et al (2021) used the IKum distribution to model the wind speed data and estimated its parameters by using the maximum product of spacings (MPS) and least squares (LS) methods. Mahdavi and Kundu (2017) used the alpha power transformation (APT) for generating a probability distribution. Dey et al (2017) obtained the alpha power generalized Exponential distribution. (i) An alpha power inverted Kumaraswamy (APIK) distribution is introduced as an alternative to the IKum and some of its extended/generalized versions such as the MOEIK and GIKw-W distributions.
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