The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

Abstract

In this paper, we propose a generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter. We motivate this generalization by presenting theoretical and practical gains, both consequences of new flexible symmetric/asymmetric properties in a wide sense. Our main mathematical results are about stochastic ordering, uni/multimodality analysis, series expansions of crucial probability functions, probability weighted moments, raw and central moments, order statistics, and the maximum likelihood method. The special member of the family defined with the inverse Weibull distribution as baseline is highlighted. It constitutes a new four-parameter lifetime distribution which brightensby the multitude of different shapes of the corresponding probability density and hazard rate functions. Then, we use it for modelling purposes. In particular, a complete numerical study is performed, showing the efficiency of the corresponding maximum likelihood estimates by simulation work, and fitting three practical data sets, with fair comparison to six notable models of the literature.

A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family

“…where γ(a, b) = a 0 x b−1 e −x dx denotes the lower incomplete gamma function. Subsequently, using Equations (10), (21), and (26) in Equation (25), the µ(t), according to the APEWED, is obtained by…”

“…We compared the fit of the APEWED with some other distributions; namely, Kumaraswamy Weibull (Ku-W) by [22], beta Weibull (BW) by [23], exponentiated generalized Weibull (EGW) by [24], alpha power inverted exponential (APIE) by [25], exponential (E) and exponentiated truncated inverse Weibull-inverse Weibull (ETIWIW) by [26].…”

New Method for Generating New Families of Distributions

“…where I is given by (23). Thus, by substituting (10) and ( 23) into Equation (25),μ(t) can be derived as follows…”

The Exponentiated Fréchet Generator of Distributions with Applications

“…Recently, new families have been introduced in the literature: the odd Fréchet-G [9], extended odd Fréchet-G [10], Fréchet Topp Leone-G [11], type II power Topp-Leone by [12], and exponentiated truncated inverse Weibull-G by [13].…”