Statistical Inference of Truncated Cauchy Power-Inverted Topp–Leone Distribution under Hybrid Censored Scheme with Applications

Abstract

In this article, a new two-parameter model called the truncated Cauchy power-inverted Topp–Leone (TCP-ITL) is constructed by merging the truncated Cauchy power -G (TCP-G) family with the inverted Topp–Leone (ITL) distribution. Some structural properties of the newly suggested model are obtained. Different types of entropies are proposed under the TCP-ITL distribution. Under the complete and hybrid censored data, the maximum likelihood (ML), maximum product of spacing (MPSP), and Bayesian estimate approaches are explored. A simulation study is developed to test the proposed distribution’s restricted sample attributes. In the majority of cases, the numerical data revealed that the Bayesian estimates provided more accurate outcomes than the equivalent alternative estimates. The adaptability of the proposed approach is proven using examples from dependability, medicine, and engineering. A real-world data set is utilized to demonstrate the potential of the TCP-ITL distribution in comparison to other well-known distributions. The results of the model selection revealed that the proposed distribution is the best choice for the data sets under consideration.

Kernel Construction for Exploring Trends in Probability Distribution Development

“…In the next illustration, we exemplify the case of left censoring 𝑙 𝑐𝑠 using the product kernel in equation ( 8 ; 𝑥 > 0, 𝜃 > 0 (10) where Г[−𝜃, 1] is an incomplete gamma function.…”

A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications

“…We specify them as follows: (i) It is a very simple distribution with a closed form for its CDF; (ii) its PDF and HRF are unimodal and right-skewed; (iii) it has a closed form for the mode and quantiles, and these open the door for more statistical properties; (iv) since it has a single shape parameter, it is interesting for statisticians to use it in inference using different methods. In light these qualities, many authors considered Equations ( 3) and (4) to investigate new extensions of the ITL distribution, such as the new exponential ITL [15], new ITL [16] and truncated Cauchy power ITL [17] distributions.…”

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.…”