Abstract
This note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.
Highlights
Introduction and motivationThe continuous probability distributions with bounded support are always a treasure for applied statisticians
In the literature of reliability and survival analysis, lifetime distributions with unbounded support are very large in number, but not much work is available in the case of support equal to (0, 1)
2 Properties Here, we examine some fundamental properties of the Arccos distribution
Summary
The continuous probability distributions with bounded support are always a treasure for applied statisticians. Model all potential characteristics with unit values efficiently; novel distributions with unique properties still have a place In this context, we consider an interesting new distribution with support equal to (0, 1), just like the beta and Kumaraswamy distributions. We consider an interesting new distribution with support equal to (0, 1), just like the beta and Kumaraswamy distributions It has many of the same properties as the existing distributions but has some benefits in terms of flexibility. Power distribution is important in lifetime data analysis, in environmental policy, public health, and financial engineering In this regard, we may refer the reader to [4,15].
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