Abstract
In this work, we provide a new generated class of models, namely, the extended generalized inverted Kumaraswamy generated (EGIKw-G) family of distributions. Several structural properties (survival function (sf), hazard rate function (hrf), reverse hazard rate function (rhrf), quantile function (qf) and median, sth raw moment, generating function, mean deviation (md), etc.) are provided. The estimates for parameters of new G class are derived via maximum likelihood estimation (MLE) method. The special models of the proposed class are discussed, and particular attention is given to one special model, the extended generalized inverted Kumaraswamy Burr XII (EGIKw-Burr XII) model. Estimators are evaluated via a Monte Carlo simulation (MCS). The superiority of EGIKw-Burr XII model is proved using a lifetime data applications.
Highlights
Study of data is the most important and fundamental topic in statistics. e probability distributions help in the characterization of the variability and uncertainty prevailing in data by identifying the patterns of variation. e objective of statistical modeling is to develop appropriate probability distributions that adequately explain a data set generated by surveys, observational studies, experiment, etc.In this context, there have been fundamental and significant thriving in probability distribution theory via the introduction of new generalized families of distributions, and several techniques to develop new distributions have been proposed
In this part of paper, we offer a brief discussion on some of the other basic functions related to the extended generalized inverted Kumaraswamy generated (EGIKw-G) class of models including the pdf, the sf, the hrf, the rhrf, and the cumulative hazard rate function which have an important role in reliability theory
Structural Properties of EGIKw-G Family of Distributions. In this part of article, we provide some useful expressions for EGIKw-G class including explicit expansions of density and cumulative distribution function, rth moment, m d, moment generating function, and pdf of order statistics
Summary
Study of data is the most important and fundamental topic in statistics. e probability distributions help in the characterization of the variability and uncertainty prevailing in data by identifying the patterns of variation. e objective of statistical modeling is to develop appropriate probability distributions that adequately explain a data set generated by surveys, observational studies, experiment, etc. E objective of statistical modeling is to develop appropriate probability distributions that adequately explain a data set generated by surveys, observational studies, experiment, etc. In this context, there have been fundamental and significant thriving in probability distribution theory via the introduction of new generalized families of distributions, and several techniques to develop new distributions have been proposed. Let s(t) denote the expression for pdf of some random variable (rv), T ∈ [a, b], where − ∞ ≤ a < b < ∞, and consider D[W(x)] is some function of cdf of another rv, say X; the T-X family can be defined as.
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