Abstract
A bounded form of the Teissier distribution, namely the unit Teissier distribution, is introduced. It is subjected to a thorough examination of its important properties, including shape analysis of the main functions, analytical expression for moments based on upper incomplete gamma function, incomplete moments, probability-weighted moments, and quantile function. The uncertainty measures Shannon entropy and extropy are also performed. The maximum likelihood estimation, least square estimation, weighted least square estimation, and Bayesian estimation methods are used to estimate the parameters of the model, and their respective performances are assessed via a simulation study. Finally, the competency of the proposed model is illustrated by using two data sets from diverse fields.
Highlights
The introduction of new statistical distributions, defined on both the whole real line and the positive real line, is required for the interpretation of real-world occurrences
In the recent past, some authors have focused on developing distributions that are defined on the bounded interval using any one of the parent distribution transformation techniques
In order to obtain an overview of the shapes of the pdf (2) and hrf (4), the corresponding plots for different choices of the parameter θ are given in Figures 1 and 2, respectively
Summary
The introduction of new statistical distributions, defined on both the whole real line and the positive real line, is required for the interpretation of real-world occurrences. In the former case, there is a tremendous amount of work in the literature on various models, such as [24,25,26] As far as the latter case is considered, the papers in [8,27] showed that the unit inverse Gaussian and logit slash distributions, respectively, provide a bathtub-shaped hrf. These two distributions are more intricate because of the presence of the log function in their pdfs, and so their cdfs are not obtained in closed form.
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