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. 2022 Jul 27;24(8):1033.
doi: 10.3390/e24081033.

Inference for a Kavya-Manoharan Inverse Length Biased Exponential Distribution under Progressive-Stress Model Based on Progressive Type-II Censoring

Naif Alotaibi  1 , Atef F Hashem  1   2 , Ibrahim Elbatal  1 , Salem A Alyami  1 , A S Al-Moisheer  3 , Mohammed Elgarhy  4
Affiliations

Inference for a Kavya-Manoharan Inverse Length Biased Exponential Distribution under Progressive-Stress Model Based on Progressive Type-II Censoring

Naif Alotaibi et al. Entropy (Basel). .

Abstract

In this article, a new one parameter survival model is proposed using the Kavya-Manoharan (KM) transformation family and the inverse length biased exponential (ILBE) distribution. Statistical properties are obtained: quantiles, moments, incomplete moments and moment generating function. Different types of entropies such as Rényi entropy, Tsallis entropy, Havrda and Charvat entropy and Arimoto entropy are computed. Different measures of extropy such as extropy, cumulative residual extropy and the negative cumulative residual extropy are computed. When the lifetime of the item under use is assumed to follow the Kavya-Manoharan inverse length biased exponential (KMILBE) distribution, the progressive-stress accelerated life tests are considered. Some estimating approaches, such as the maximum likelihood, maximum product of spacing, least squares, and weighted least square estimations, are taken into account while using progressive type-II censoring. Furthermore, interval estimation is accomplished by determining the parameters' approximate confidence intervals. The performance of the estimation approaches is investigated using Monte Carlo simulation. The relevance and flexibility of the model are demonstrated using two real datasets. The distribution is very flexible, and it outperforms many known distributions such as the inverse length biased, the inverse Lindley model, the Lindley, the inverse exponential, the sine inverse exponential and the sine inverse Rayleigh model.

Keywords: Kavya–Manoharan class of distributions; inverse length biased exponential distribution; maximum likelihood estimation; maximum product spacing; progressive censoring; progressive-stress model.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The process of generating order statistics under progressive type-II censoring.
Figure 2
Figure 2
Different shapes of pdf for KMILBE distribution.
Figure 3
Figure 3
Different shapes of hrf for KMILBE distribution.
Figure 4
Figure 4
The fitted cdf plots for the data set 1.
Figure 5
Figure 5
The fitted cdf plots for data set 2.
Figure 6
Figure 6
The fitted pdf plots for the data set 1.
Figure 7
Figure 7
The fitted pdf plots for data set 2.
Figure 8
Figure 8
The fitted sf plots for data set 1.
Figure 9
Figure 9
The fitted sf plots for data set 2.
Figure 10
Figure 10
The P-P plots of the competing continuous models for data set 1.
Figure 11
Figure 11
The P-P plots of the competing continuous models for data set 2.
See this image and copyright information in PMC

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