A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

Abstract

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique. We refer to the new model as modified alpha power transformed Weibull distribution. The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions, which are quite familiar in environmental investigations. Its hazard rate function can be decreasing, increasing, bathtub and upside-down then bathtub shaped. Diverse structural properties of the proposed model are acquired including quantile function, moments, entropies, order statistics, residual life and reversed failure rate function. The parameters of the distribution were estimated using the maximum likelihood function. The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed. Via a simulation study, the performance of the point and interval estimates are compared using different criteria. Employing real lifetime data sets, we verify that the offered model furnishes a better fit than some other lifetime models including Weibull, gamma and alpha power Weibull models.

New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression

“…If a random variable X follows the MAPTBXII, then the PDF can be obtained by substituting equation (3) into equation ( 2), while the CDF can be obtained by substituting equation (4) into equation (1). Te CDF and PDF of the MAPTBXII can then be expressed, respectively, as follows:…”

“…Tis parameter introduction has been shown to improve the ability of the developed distributions to ft varied real-life datasets with high degrees of skewness and kurtosis. Some of these newly developed distributions include the modifed alpha power transformed Weibull [1], general two-parameter [2], truncated inverse power Ailamujia [3], half-logistic modifed Kies exponential [4], truncated inverse power Lindley [5], Marshall-Olkin-Weibull-Burr XII [6], generalised unit half-logistic geometric [7], Chen Burr-Hatke exponential [8], modifed XLindley [9], arctan power [10], harmonic mixture Fréchet [11], sine-Weibull geometric [12], bounded odd inverse Pareto exponential [13], new extended Chen [14], power XLindley [15], extended Poisson-Fréchet [16], exponentiated Fréchet loss [17], Gompertz-Makeham [18], and logistic exponential [19] distributions.…”

Reliability Analysis and Applications of Generalized Type-II Progressively Hybrid Maxwell–Boltzmann Censored Data

“…These breakdowns do not cause aircraft damage, but they do require the repair of a windscreen. This application provides an analysis of a data set, reported by Murthy et al [39] and rediscussed by Alotaibi et al [40], representing 84 failure time points of aircraft windshields, see Table 2. To demonstrate whether aircraft windshields data fit the MB distribution or not, the Kolmogorov-Smirnov (K-S) statistic (along with its p-value) is obtained.…”

Modified Alpha Power Transformed Inverse Power Lomax Distribution with appllications

“…This refined method introduces an additional term, enabling greater customization and refinement in modeling diverse datasets. Expanding upon the MAPT framework, researchers have devised a range of distributions, including the Modified Alpha Power Transformed Weibull Distribution [56].…”