Garhy distribution with Different Estimation Methods and Applications to Engineering and Medical Data

In this article, we introduce and investigate a new one-parameter mixture distribution called the “Garhy distribution”. The probability density function is very adaptable, as it may take on right skewed, unimodal, and heavy tailed patterns. In addition, the hazard rate function indicates that data with increasing shaped failure rates may be adapted by the Garhy distribution. Several fundamental statistical and mathematical properties are calculated including mode, quantile function, moments, mean, variance, skewness, kurtosis, moment-generating function, incomplete moments, inequality measures, order statistics, and extropy measures. The scale parameter of the Garhy distribution is estimated employing twelve different estimation approaches, maximum likelihood, maximum product of spacings, least-squares, weighted least-squares, Anderson darling, right-tail Anderson darling, left-tail Anderson darling, Cramér von-Misses, and the least-squares method. The effectiveness of these strategies is evaluated using a detailed simulation study. Furthermore, we used the Garhy distribution to examine two real-world data sets, demonstrating its superior performance compared to specific competitors.