A Note on Topp-Leone Odd Log-Logistic Inverse Exponential Distribution

Abstract

The inverse exponential distribution is widely used in the field of reliability. In this article, we present a generalization of the inverse exponential distribution in formation of Topp-Leone odd log-logistic inverse exponential distribution. We provide a comprehensive account of some mathematical properties of the Topp-Leone odd log-logistic inverse exponential distribution. The possible shapes of the corresponding probability density function and hazard function are obtained and graphical demonstration are presented. The distribution is found to be unimodal. The results for moment, moment-generating function, and probability-generating function are computed. The residual and reversed residual functions are also obtained. The proposed method of maximum likelihood is used for the estimation of model parameters. The performance of the parameters is investigated through simulation. The usefulness of the proposed model is illustrated by means of a real data set.

A unified exponential-H family for modeling real-life data: Properties and inference

“…In this section, the importance and applicability of the NExW distribution are addressed using three real-life data sets. We compare the fit of the NExW distribution with its competing Weibull extensions including the alpha power-Weibull (APW) [15] , exponentiated-Weibull (EW) [16] , inverse-Weibull (IW) [17] , odd Burr-III Weibull (OBIIIW) [18] , Topp–Leone inverse-Weibull (TLIW) [19] distributions.…”

Bayesian inference for the inverse Weibull distribution based on symmetric and asymmetric balanced loss functions with application

“…Abbas et al [2] established the Topp Leone IWD, while Shuaib et al [52] generalised the IWD for lifespan modelling.…”

“…Specifically, for the Balanced Squared Error (BSE) loss function, we opt for 𝜌(𝜙, 𝜙 ̂) = (𝜙 ̂− 𝜙) 2 , resulting in the following expression:…”

“…This balanced loss function can be tailored to various loss functions, including absolute value, squared error, LINEX, and general entropy loss functions. By choosing the loss function as 𝜌(𝜙, 𝜙 ̂) = (𝜙 ̂− 𝜙) 2 , equation ( 14) simplifies to the BSE loss function in the following manner:…”

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

“…Generalizations of the TL distribution have been shown to be beneficial in a variety of disciplines. Many notable academics have made significant attempts to suggest new generalized and developed modifications of the TL model, for example, TL inverse Weibull distribution [2], Type I half-Logistic TL distribution [3], TL geometric distribution [4], truncated Cauchy power inverted TL distribution [5], TL Nadarajah-Haghighi distribution [6], power inverted TL distribution [7], TL linear exponential distribution [8], Kumaraswamy inverted TL distribution [9], new power TL family [10], alpha power inverted TL distribution [11], half-logistic inverted TL distribution [12], type II Power TL family [13], odd log-logistic TL family [14], TL odd Fréchet distribution [15], Burr III-TL family [16], inverse TL distribution [17], exponentiated generalized TL family [18], transmuted TL power function distribution [19], transmuted TL family [20], sine TL family [21], weighted TL family [22], TL inverse Lomax distribution [23], and new weighted TL family [24], among others.…”