Statistical Modeling using A New Hybrid Form of The Inverted Exponential Distribution with Different Estimation Methods

Abstract

This paper introduces a new four-parameter distribution called the exponentiated Gompertz generated inverted exponential (EGGIE) distribution. Explicit expressions of the structural properties such as the ordinary and incomplete moments, probability weighted moments, quantile function, Lorenz and Bonferroni curves, entropies, and order statistics are derived. The empirical findings indicate that the maximum likelihood procedure dominates the other estimators in the simulation study while the Cramer-Von Mises procedure dominates in the two real datasets applications. We demonstrate the superiority of the EGGIE distribution over the Gompertz Lomax, odd Fréchet Inverse exponential, generalized inverse exponential, generalized inverse exponential, exponential inverse exponential, and Gompertz Weibull distribution using the maximum likelihood procedure utilizing two real datasets applications. The findings show that the EGGIE distribution yields the best goodness of fit to the two datasets. Keywords: exponentiated Gompertz generated family; inverse exponential distribution; Kolmogorov-Smirnov statistic; Anderson-Darling; maximum product spacing. Abstrak Paper ini memperkenalkan distribusi 4-parameter baru yang disebut dengan distribusi exponentiated Gompertz generated inverted exponential (EGGIE). Ekspresi eksplisit sifat struktural dari distribusi ini diturunkan, seperti momen biasa dan momen tak lengkap, momen probabilitas terboboti, fungsi kuartil, kurva Lorenz dan Bonferroni, entropi, dan statistik urutan. Temuan empiris menunjukan bahwa prosedur maksimum likelihood mendominasi estimator lainnya pada studi simulasi, sementara prosedur Cramer-Von Mises mendominasi pada aplikasi dua dataset nyata. Peneliti menunjukkan keunggulan dari distribusi EGGIE dibandingkan distribusi Gompertz Lomax, odd Frechet Inverse exponential, generalized inverse exponential, exponential inverse exponential, dan Gompertz Weibull menggunakan metode maksimum likelihood yang diaplikasikan pada dua dataset nyata. Hasil menunjukan bahwa distribusi EGGIE menghasilkan kecocokan model yang baik pada kedua dataset. Kata Kunci: keluarga bangkitan exponentiated Gompertz; distribusi inverse exponential; Kolmogorov-Smirnov statistic; Anderson-Darling; maximum product spacing. 2020MSC: 62E10

Keywords

• exponentiated gompertz generated family
• inverse exponential distribution
• kolmogorov-smirnov statistic
• anderson-darling
• maximum product spacing.