The Generalized Additive Weibull-G Family of Distributions

Abstract

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

On the Exponentiated Weibull Rayleigh Distribution

“…The estimators that are obtained based on this procedure enjoy desirable asypmtotic properties and therefore they are often utilized to obtain confidence intervals (CI) and test of statistical hypotheses. Suppose that 1 ,, n xx be an observed random sample from the EWR distribution with pdf (6). Then the log-likelihood function, denoted by ln , for the  approximately possesses a 4-variate normal distribution with the mean   and the variance-covariance matrix I -1 ( where I -1 ( is the inverse matrix of I( This property of ML estimators can be used to obtain approximate CI for the model parameters.…”

“…In recent times, diverse statisticians exploered some new generated families of distributions by incorporate one or more extra shape parameter(s) to the baseline model to yield new flexible distributions. Some of the generated families are: the beta-G [1], Kumaraswamy (Kw)-G [2], Weibull-G [3], Garhy-G [4], exponentiated Weibull-G (EW-G) [5], additive Weibull-G [6], Kw Weibull-G [7], Type II half logistic-G [8] and exponentiated extended-G [9] among others.…”

“…Let X : ∞ be a continuous r.v. The pdf of X for a = 1, is(6) if and only if its hrf hF (x) verifies the differential equation…”

“…The r.v. X has pdf(6) if and only if its reversed hrf If X has pdf (6), then clearly the above differential equation holds. That is from which, we have, for x > 0…”

A new generalization of Weibull-exponential distribution with application

“…These families have been obtained by introducing one or more additional shape parameter(s) to the baseline distribution. Some of the generated families are: the beta-G [12,19], gamma-G (type 1) [27], Kumaraswamy-G (Kw-G) [6], McDonald-G (Mc-G) [2], gamma-G (type 2) [25], transformed-transformer (T-X) [4], Weibull-G [5], Kumaraswamy odd log-logistic [3], Garhy-G [9], exponentiated Weibull-G [14,15] introduced a new family called Kumaraswamy Weibull-generated, The additive Weibull-G [17], type II half logistic-G [10,16] introduced exponentiated extended-G family. The cumulative distribution function (cdf ) of Kumaraswamy Weibull-generated family is given by…”