Abstract
The rT - X family of distributions induced by V which have been introduced in [1] is further explored in this paper. In particular, we have obtained some basic mathematical properties of this new family. The simulation study shows the method of maximum likelihood is adequate in estimating the unknown parameters in sub-models of this new class of statistical distributions. Further, the application shows that sub-models of this new family of distributions are useful in material science engineering and related disciplines that call for modeling and forecasting of related data sets. Finally, inspired by the Ampadu-G family of distributions [2], we propose a new class of distributions that have never appeared in the literature, and ask the reader to investigate some properties and applications of this new class of distributions.
Highlights
Introduction and PreliminariesWe begin by recalling the rT − X family of distributions induced by V which have been introduced in [1]
The PDF of the approximated new rT − X family of distributions of type I is given by j2 (x) = rT (F (x)) f (x), where the random variable T with support [0, ∞) has PDF rT, and the random variable X has CDF F (x) and PDF f (x)
If a random variable Y has CDF given by the new Exponential-Weibull distribution of type I, we write
Summary
We begin by recalling the rT − X family of distributions induced by V which have been introduced in [1]. Clement Boateng Ampadu and Abdulzeid Yen Anafo family of distributions of type I, if the CDF can be expressed as the following integral. (t dt, where the random variable X has CDF F(x), and the random variable T with support [0, ∞) has quantile density qT and CDF RT , ProductLog[z] gives the principal solution for w in z = wew, and α > 0. The CDF of the new rT − X family of distributions of type I is given by. Where the random variable T with support [0, ∞) has CDF RT , ProductLog[z] gives the principal solution for w in z = wew, and the random variable X has CDF F(x). By differentiating the CDF above, the PDF of the new rT − X family of distributions of type I can be obtained
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