Abstract
In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.
Highlights
In the last few decades, many efforts have been made to improve the modelling of different types of data arising from several fields such as actuarial, environmental, economics, engineering, medicine and biological sciences
The first data set consists the fatigue time of 101 6061-T6 Aluminum Coupons (AmCs) cut parallel to the direction of rolling and oscillated at 18 cycles per second, see Birnbaum and Saunders [39]. We have used this data to show the fitting capability of the Type I HLOWFr model relative to some other competing models such as Topp-Leone Fr (ToLFr), transmuted Fr (TrFr), exponentiated TrFr (ETrFr), Gumble Fr (GuFr), type I generalized Fr (TIGFr), exponentiated
We have proposed a new generator of univariate continuous distributions, called Type I HLOW-G family
Summary
In the last few decades, many efforts have been made to improve the modelling of different types of data arising from several fields such as actuarial, environmental, economics, engineering, medicine and biological sciences. Zaidi et al [17] invented a new class named as log-logistic tan generalized family They showed that the special models of this family can assume a variety of shapes for density and hazard function. The main objectives of proposing the Type I HLOW-G family can be stated as follows: to list the special distributions containing different shaped HRF (increasing, decreasing, unimodal, and Bathtub); to provide more flexibility for skewness and kurtosis as compared to the baseline model; to consistently produce superior fits as compared to other generated distributions with the same baseline model; and to illustrate how different estimators of the unknown parameters of the particular sub-model perform for varied sample size and various combinations of the parametric values.
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