Parameter Estimation for the Linear Hazard Rate Distribution Based on Records and Inter-record Times

The linear hazard rate distribution (LHRD) is a two-parameter distribution that contains exponential and generalized Rayleigh distributions as special cases. It has applications in a number of fields including reliability improvement, life testing, and survival analysis. An iterative EM algorithm is presented to compute maximum likelihood estimates (MLEs) for the LHRD based on records and inter-record times. Simulation results indicate that the estimates obtained by maximum likelihood method are better than those obtained by the least-squares type estimation and by the elemental percentile method. We also evaluate the expected values and variances of the MLEs for various sample sizes in order to determine the unbiasing factors of the MLEs which can be utilized in performing tests of exponentiality and also for examining the appropriateness of Rayleigh model to data at hand.