WEIGHTED INTERVENED EXPONENTIAL DISTRIBUTION AS A LIFETIME DISTRIBUTION.

This study proposes and investigates the weighted intervened exponential distribution, which is demonstrated as a generalized extension of the intervened exponential distribution. The form of the weighted intervened exponential distribution is obtained by considering a specific non-negative weighted function. The probability density function and cumulative density function of the proposed model are given, and its generalized form of reliability function and the hazard rate function is also derived. By choosing a different set of parametric values, the graphical demonstrations of the probability density function of weighted intervened exponential distribution are given where it acquires different curve shapes. The weighted intervened exponential distribution density function is then further studied in the limited form as a special case called the length-biased intervened exponential distribution. Along with the distribution of order statistics, stochastic ordering, stress-strength reliability, and entropy measure, several distributional and reliability aspects of the length-biased intervened exponential distribution are derived. For estimating the unidentified parameters of the length-biased variant, the most suggested approach known as the maximum likelihood estimation technique is implemented. To explore the behavior of the parameter estimates for various sample sizes, a sample data generation technique is required to carry out the process. Since the quantile function of the length biased intervened exponential distribution is not in closed form. So, the alternative data generation algorithm is employed which is known as the acceptance-rejection algorithm technique, and a Monte-Carlo simulation study is done. The absolute average bias and mean square error of the estimated parameters of the length-biased version model are calculated and it is noticed that both the calculated measures decrease simultaneously on increasing the sample size. In order to determine if the model is appropriate, a real-life time-to-event data set is examined as an example, and length biased distribution is juxtaposed with several other common available lifetime distributions for comparison purposes. [ABSTRACT FROM AUTHOR]

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