Abstract
We introduce a new generalized transmuted-Weibull distribution and studied some of the mathematical characterizations of the new distribution. The quantile function, entropy, moment, moment generating function, and order statistics of the distribution are derived. The unknown parameters of the distribution were estimated through the maximum likelihood approach. The potential and flexibility of the new generalized transmuted-Weibull are illustrated by comparing it with other known distribution using real-life data sets. Â
Highlights
The Weibull distribution has gained a wide range of applicability in modelling data in reliability, engineering, biological, and risk studies
Let x1, x2, ... , xn be a random sample from AGT-W distribution such that x1 < x2 < ⋯ < xn, the pdf of the ith order statistics denoted by f(xi:n) is given by f(xi:n) n! (i−1)!(n−i)!
We studied the some mathematical characterizations including the shape, hazard rate function, non-central moment, mgf, entropy, and order statistic of four-parameter AGT-W distribution
Summary
The Weibull distribution has gained a wide range of applicability in modelling data in reliability, engineering, biological, and risk studies. The addition of parameter(s) to already existing (classical) distributions to generate family of distributions extends and provides more flexibility to the classical distributions in modelling data which ordinarily would have not provided a good fit. The main motivations of this paper are to propose a more flexible extension of Weibull distribution that can model bathtub, reversedbathtub, unimodal, increasing and decreasing hazard rate shapes. The remainder of the paper is organised as follows; Section 2, introduced the new distribution and its sub-models. The ordered statistics of the new distribution was considered, while in Sections 5 and 6, the method of parameter estimation and applications of the distribution on two real-life data sets were presented
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