Theoretical properties of a new survival distribution based upon the renowned distribution has been proposed, such as the probability density function, the cumulative distribution function, the \(r^{th}\) ordinary moment, the moment generating function, the incomplete moments, the survival function, the hazard rate function, the mode, and the asymptotic behavior. This new distribution is called the new mixture of generalized gamma distribution. In addition, the maximum likelihood estimator of an unknown parameter has been studied. Finally, to illustrate usefulness of the proposed distribution, the model has been applied in describing actual data sets.

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), $r^{th}$ 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.

In the past few decades, numerous efforts have been made to develop a new class of lifetime distributions with greater flexibility by extending known distributions. In this paper, the two popular distributions, Nakagami and Rayleigh, were selected and combined to create a new distribution, namely the Nakagami–Rayleigh (NK-R) distribution, to obtain a distribution that was better than each other. First, its probability density and cumulative function expressions were initially derived. Then, some distributional properties such as survival function, hazard function, moment generating function, and order statistics were investigated. Next, the parameters were estimated by the maximum likelihood method, and their performance was evaluated via a simulation study with varying parameter values and sample sizes. Finally, the proposed distribution has been fitted to a real-life data set to examine its potential and flexibility. The results indicated that the offered estimators performed nicely. Furthermore, based on the Akaike information criterion, the proposed distribution provided a more appropriate model than other candidate distributions in terms of goodness of fit.

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.

In this article, a four-parameter Nakagami Weibull distributions (NW) is proposed. We study a few statistical properties such as quantile function, moments, moment generating function, entropy, and order statistics have been derived. The maximum likelihood estimate is used to estimate the parameter of the NW distribution. We fit the proposed NW distribution to a real-life data set to examine its potential and flexibility. Our findings showed that the NW distribution performs much better than its competitors, with favorable comparisons to existing distributions in terms of goodness-of-fit.

This article proposes the new Nakagami-generated family of distribution (NNak-G) and the new Nakagami-Exponential (NNak-E) distribution for fitting skewed and heavy-tailed data. By integrating the flexibility of the Nakagami distribution with the useful properties of the exponential distribution, the NNak-E distribution provides enhanced adaptability for fitting with right-skewed data structures. The theoretical properties of the NNak-E distribution are developed, including its distribution function, density function, moments, and hazard function. Parameter estimation is constructed using the Maximum Likelihood Estimation (MLE) method, and a comprehensive simulation study is performed to evaluate the performance of the MLE estimates. Furthermore, the NNak-E distribution is applied to real-world datasets, where it demonstrates superior goodness-of-fit compared to existing distributions. The results confirm that NNak-E is a choice distribution for practitioners and researchers dealing with asymmetric and heavy-tailed data distributions in diverse fields such as engineering, medical research, and risk assessment.