Properties and Maximum Likelihood Estimation of the Novel Mixture of Fréchet Distribution

In recent decades, there have been numerous endeavors to develop a novel category of survival distributions possessing enhanced flexibility through the extension of existing distributions. This article constructs and validates the statistical properties of a novel survival distribution in order to obtain an alternative distribution that is suitable for analyzing survival data by presenting the novel mixture of the Fréchet distribution along with statistical properties such as the probability density function (PDF), cumulative distribution function (CDF), rth ordinary moment, skewness, kurtosis, moment-generating function, mean, variance, mode, survival function, hazard function, and asymptotic behavior, as well as constructing the estimators of the unknown parameter by employing the expectation-maximization (EM) algorithm, and simulated annealing. Additionally, the performance of the proposed estimators was compared with bias, mean squared errors (MSE), and simulated variances, and given an illustrative example of the proposed distribution to the survival data set in order to show that the proposed distribution is appropriate for the right-skewed data. This will be extremely advantageous in survival analysis.