A New Family of Distributions to Encounter the Extrapolating Issues

Abstract

Traditionally, infinite models have been fitted on finite datasets which extrapolate the data, resulting in inadequate model fitting and predictions. To overcome this problem, we develop a new family of truncated distributions by introducing a new generator. In this article, a truncated random variable $X_{tr}$ “the transformer or input” is exerted to transform another random variable T “transformed or generator,” which yields a new $T-X_{tr}$ family of distributions. Several characteristics of $T-X_{tr}$ family of distributions are provided which are equally useful in engineering and biological sciences. For application purposes, a type-2 Gumbel-truncated exponential distribution is generated by using the proposed method along with its statistical properties. The efficacy of the new model is demonstrated by applying it to echophysiology and comparing the resulting outputs with those from the baseline models. Relevance of the Work. Indeed, the probability models have infinite domains but they are applied on the finite real datasets which may lead to exaggerated inferences and predictions. This problem can be solved by developing models that have finite domains. We propose finite models to analyze the finite data proficiently, provide reliable inferences, and save time.