Abstract

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

Highlights

  • Several statistical distributions have been extensively applied to describe and predict existing phenomena in several disciplines, such as economics, engineering, finance, insurance, demography, biology, and environmental and medical sciences

  • This paper introduces a new distribution, named the alpha power Weibull–exponential distribution (APWED), based on a novel technique for generating new distributions with more flexibility in modeling real data in a variety of fields

  • To examine the validity of the proposed model, in comparison with the other models, we considered the following goodness-of-fit (GOF) criteria: The negative −` θ, Akaike’s information Criterion (AIC), the Corrected Akaike Information Criterion (CAIC), the Hannan–Quinn Information Criterion (HQIC), Anderson–Darling (A), Cramer–von Mises (W), and Kolmogorov–Smirnov (K–S) statistics

Read more

Summary

Introduction

Several statistical distributions have been extensively applied to describe and predict existing phenomena in several disciplines, such as economics, engineering, finance, insurance, demography, biology, and environmental and medical sciences. Many researchers have attempted to extend these existing classical distributions, in order to obtain greater flexibility in modeling data from different fields of study. Various methods for generating new families of distributions have been studied recently. The auhtors of [6] developed a general method, called the transformed–transformer (T–X) family of distributions, which enable the use of any continuous distribution as the generator. This paper introduces a new distribution, named the alpha power Weibull–exponential distribution (APWED), based on a novel technique for generating new distributions with more flexibility in modeling real data in a variety of fields.

The Alpha Power Weibull—Exponential Distribution
Special Cases of the APWED
Mean Residual Life and Mean Waiting Time
Rényi and Shannon Entropies
Maximum Likelihood Estimates
Simulation Study
Strength Data
Conclusions
Methods
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call