On a Modified Weighted Exponential Distribution with Applications

Abstract

Practitioners in all applied domains value simple and adaptable lifetime distributions. They make it possible to create statistical models that are relatively easy to manage. A novel simple lifetime distribution with two parameters is proposed in this article. It is based on a parametric mixture of the exponential and weighted exponential distributions, with a mixture weight depending on a parameter of the involved distribution; no extra parameter is added in this mixture operation. It can also be viewed as a special generalized mixture of two exponential distributions. This decision is based on sound mathematical and physical reasoning; the weight modification allows us to combine some joint properties of the exponential and weighted exponential distribution, which are known as complementary in several modeling aspects. As a result, the proposed distribution may have a decreasing or unimodal probability density function and possess the demanded increasing hazard rate property. Other properties are studied, such as the moments, Bonferroni and Lorenz curves, Rényi entropy, stress-strength reliability, and mean residual life function. Subsequently, a part is devoted to the associated model, which demonstrates how it can be used in a real-world statistical scenario involving data. In this regard, we demonstrate how the estimated model performs well using five different estimation methods and simulated data. The analysis of two data sets demonstrates these excellent results. The new model is compared to the weighted exponential, Weibull, gamma, and generalized exponential models for performance. The obtained comparison results are overwhelmingly in favor of the proposed model according to some standard criteria.

The Inverse-Power Burr–Hatke-G Family: Properties and Inference with Real-Life Applications

“…The IPBHEx distribution is fitted and compared with some competitive models namely: the exponential (Ex), Marshall-Olkin exponential (MOEx) [22], exponentiated-exponential (EEx) [23], beta generalized exponential (BGEx) [24], Weibull-exponential (WEx) [25], alpha-power exponential (APEx) [26], modified exponential (MEx) [27], transmuted generalized-exponential (TGEx) [28], Marshall-Olkin alpha-power exponential (MOAPEx) [29], alpha power exponentiated-exponential (APEEx) [30], and modified weighted exponential (MWEx) [31].…”

Cauchy modified generalized exponential distribution: Estimation and Applications

“…(https://earthquake.usgs.gov/). 18,16,13,12,13,20,15,16,12,18,15,16,13,15,16,11,11,18,12,17,24,20,16,19,12,19,16,7,17 Table 1 shows the summary statistics of the model To examine the descriptive characteristics of the data, we generated and presented the TTT plot and boxplot in Figure 2. The boxplot indicates a positive skewness and non-normal distribution of the data.…”

“…Several innovative probability models have been created through the ~57~ modification of exponential distributions found in literature. These distributions encompass a wide range of models, including the extended exponential distribution (Gomez et al, 2014) [15] , The modified exponential (ME) distribution (Rasekhi et al, 2017) [26] , the New Odd Generalized Exponential -Exponential Distribution (Kumar & Kumar, 2019) [19] , the Marshall-Olkin generalized exponential distribution (Ristic & Kundu, 2015), the beta generalized exponential distribution (Barreto-Souza et al, 2010) [6] , the Kumaraswamy-Generalized Exponentiated Exponential Distribution (Mohammed, 2014) [22] , Modified slashed generalized exponential distribution (Astorga et al, 2020) [5] , Weibull generalized exponential distribution (Almongy et al, 2021) [3] , Twoparameter modified weighted exponential distribution (Chesneau et al, 2022) [11] , Modified upside-down bathtub-shaped hazard function distribution (Chaudhary et al, 2023) [10] , and A New Four Parameter Extended Exponential Distribution (Hassan et al, 2022) [18] . These lifetime models might exhibit a hazard rate function (HRF) with a bathtub-shaped pattern.…”

A Study on One-Parameter Entropy-Transformed Exponential Distribution and Its Application

“…In addressing the above challenges to make the exponential distribution more flexible and applicable to a wide range of real-life scenarios, several researches have proposed different transformation techniques. (Owoloko, Oguntunde and Adejumo, 2015) studied the "transmuted exponential distribution", (El-Damrawy, Teamah and El-Shiekh, 2022) derived the "Truncated bivariate Kumaraswamy exponential distribution", (Chesneau, Kumar, Khetan and Arshad, 2022) derived the "modified weighted exponential distribution", (Ozkan and Golbasi, 2023) proposed the "Generalized Marshall-Olkin exponentiated exponential distribution" amongst others. Dragan and Isaic-Maniu (2019) described the pseudo-entropic transformation also called entropy transformation by (Aziz, Husain, and Ahmed, 2021) which has some unique features.…”