In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

This article introduces a new flexible four parameter distribution by convolution of the exponential and Weibull distribution using the odd function transformation, which offers greater flexibility in terms of fit, its called the modified exponential-Weibull (MEW). The MEW model is designed to provide a more accurate description of failure time data resulting from a system with one or more failure modes and is characterized by a hazard rate (HR) that takes the shape of a bathtub due to its complexity. The moments properties, quantile function, and residual life are derived and discussed. We discussed the HR function and several distributional properties of the MEW model, and applied maximum likelihood and Bayesian techniques to estimate its unknown parameters. The Hamiltonian Monte Carlo (HMC) algorithm is employed to simulate the posterior distributions and verify the MEW Bayes estimators. We examined the behavior of the MEW model on two data sets with bathtub-shaped HR and compare it with five other popular bathtub-shaped methodologies. The results indicate that the MEW model provided the best description of the two failure time data sets, suggesting that the proposed model could be a viable candidate for solving various real-life problems.