Improved maximum likelihood estimators of the parameters of the log-exponential power distribution with applications

Abstract

Owing that ensuring true representative samples from a population is dependent on sampling via sample estimators, in this paper, we established the sample maximum likelihood (ML) estimators of the location (μ), scale (σ2) and shape (β) parameters of Log-Exponential Power Distribution (LEPD), under simple random sampling (SRS), ranked set sampling (RSS) and another introduced sampling called general RSS (GRSS). The study then obtained the Fisher information (FI) of the obtained estimators under different cases: when one parameter, two parameters and when all the parameters are unknown, for each of the sampling procedure and compute its asymptotic relative efficiency (RE). The FI estimate, when GRSS samples are obtained from ith or (ith,jth) ordered samples, were established along with its RE. Application from simulated and real life data with imperfect units ranking was used to demonstrate the relevance of the study, in terms of sampling efficiency within the shortest length of interval estimate. Application of GRSS to the Food and Agricultural Organization (FAO) projected data on cattle meat boom by 2050 was considered, the implication of the sudden increase in cattle population in Nigeria and the recommendation to prevent subsequent crises due to competition for land among farmers, herders and other populace was analytically established. Finally, the procedure was used to establish the cause of increased suicide rate in Nigeria has recently published by World Health Organization (WHO).