Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications

Liyuan Pang,Weizhong Tian,Tingting Tong,Xiangfei Chen

doi:10.3390/modelling2040041

Abstract

In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.

Highlights

Modelling 2021, 2, 776–794. https://In daily life, data related to percentage and proportion are bounded
This section describes some basic properties of the LTESL distribution, which is defined as follows
The basic statistical properties of LTESL distribution are studied in detail, including moment, mean residual life (MRL)

Summary

Introduction

Data related to percentage and proportion are bounded. For example, the proportion of charitable donations in income needs a bounded continuous distribution to describe it; see Papke and Wooldridge [1]. Pourdarvish et al [3] studied a generalization of Topp–Leone distribution referred to as the exponentiated Topp–Leone distribution They discussed many aspects of this new model, such hazard rate function, the moments, and the order statistics, and applied it to milk yield data. Showed that logit slash had a good fitting effect for high-kurtosis skewness data sets with outlier observations and that the proposed model could be an alternative to the classical bounded distributions available in the statistical literature to model percentage and proportion. The rest of the paper is organized as follows: Some important mathematical properties of the new distribution are derived, such as cdf, moment, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function.

Logit Truncated-Exponential Skew-Logistic Distribution

Maximum-Likelihood Estimation

Simulation

Applications

Discussion