The R Statistical Package and Computation of Wald Confidence Intervals for the Scale Parameter of the Weighted Mixture Generalized Gamma Distribution

The weighted mixture generalized gamma (WMGG) distribution is formed by combining two distributions, the generalized gamma distribution (GG) and the length-biased generalized gamma distribution (LGG), both of which are well-suited for analyzing lifetime data. This article focuses on the development of an R statistical package for the WMGG distribution, aiming to facilitate convenient and practical utilization. Such a package is anticipated to offer substantial advantages in medical science and engineering domains. The proposed package, denominated as WMGGD, encompasses five distinct functions: 1. Probability density function, 2. Cumulative distribution function, 3. Quantile function, 4. Random number generation, and 5. Parameter estimation function. This article presents the application of packages to construct the Wald confidence interval for a scale parameter of the WMGG distribution. The results revealed that the value of the average length in the proposed confidence interval would decrease if the sample size went up. The value of the coverage probability (CP) approaches the confidence interval coefficient of 0.95. Moreover, The real-world data sets were used to illustrate the use of the proposed package. These showed that the proposed package is efficient and simple to employ.