A New Flexible Logarithmic-X Family of Distributions with Applications to Biological Systems

Abstract

Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic- $X$ (NFLog- $X$ ) family. The suggested NFLog- $X$ family is obtained by applying the T- $X$ method together with the exponential model having the PDF $m\left(t\right)=e^{-t}$ . Based on the NFLog- $X$ approach, a three parameters probability distribution, namely, a new flexible logarithmic-Weibull (NFLog-Wei) distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog- $X$ family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog-Wei distribution. Comparisons are made between the analytical goodness-of-fit metrics of the suggested distribution. We made comparison with the (i) alpha power transformed Weibull, (ii) exponentiated Weibull, (iii) Weibull, (iv) flexible reduced logarithmic-Weibull, and (v) Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions.