Parallel Simulation-Based Classical and Bayesian Inference for the Unit Harris Extended Exponential Distribution with Reliability Applications

Abstract

Bounded observations occur in a variety of applied scenarios such as reliability probabilities, degradation measures, rates, and other functions defined on the unit interval for which flexible distributional and hazard-rate behavior are desired. This paper presents the Unit Harris Extended Exponential Distribution (UHEED), a three-parameter unit distribution derived from the Harris Extended Exponential Distribution to offer more flexibility in these types of data, including the ability to model bathtub-shaped hazard rates. Several mathematical properties are developed, such as parameter identifiability, quantile elasticity, moments, order statistics, and Shannon entropy. Maximum likelihood estimation is used as classical inference; the squared error and LINEX loss functions are used to develop the Bayesian estimation with a Metropolis–Hastings within Gibbs algorithm. A representative-point approximation is also proposed for evaluating important distributional quantities, including moments and reliability measures. The Monte Carlo results indicate that the more samples, the more accurate the results of the estimation. A useful example of the UHEED is presented with naturally bounded bramble cane spatial-coordinate data, and goodness-of-fit comparisons show that it performs competitively relative to the competing unit distributions used in the analysis.