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This paper first introduces the Kerridge inaccuracy measure as an extension of the Shannon entropy and then the measure of past inaccuracy has been rewritten based on the concept of quantile function. Then, some characterizations results for lifetimes with proportional reversed hazard model property based on quantile past inaccuracy measure are obtained. Also, the class of lifetimes with increasing (decreasing) quantile past inaccuracy property and some of its properties are studied. In addition, via an example of real data, the application of quantile inaccuracy measure is illustrated.

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In this article, we consider the estimation of R{r,k}= P(X{r:n1} < Y{k:n2}), when the stress X and strength Y are two independent random variables from inverse Exponential distributions with unknown different scale parameters. R{r,k} is estimated using the maximum likelihood estimation method, and also, the asymptotic confidence interval is obtained. Simulation studies and the performance of this model for two real data sets are presented.


 

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This article considers the stress-strength reliability of a coherent system in the state of stress at the component level. The coherent series, parallel and radar systems are investigated. For 2-component series or parallel systems and radar systems, this reliability based on Exponential distribution is estimated by maximum likelihood, uniformly minimum variance unbiased and Bayes methods. Also, simulation studies have been done to check estimators' performance, and real data are analyzed.
 

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Researchers develop generalized families of distributions to better model data in fields like risk management, economics, and insurance. In this paper, a new distribution, the Extended Exponential Log-Logistic Distribution, is introduced, which belongs to the class of heavy-tailed distributions. Some statistical properties of the model, including moments, moment-generating function, entropy, and economic inequality curves, are derived. Six estimation methods are proposed for estimating the model parameters, and the performance of these methods is evaluated using randomly generated datasets. Additionally, several insurance-related measures, including Value at Risk, Tail Value at Risk, Tail Variance, and Tail Variance Premium, are calculated. Finally, two real insurance datasets are employed, showing that the proposed model fits the data better than many existing related models.