1. A Comparison Between Two Shape Parameters Estimators for (Burr-XII) Distribution
- Author
-
Shurooq Ahmed Kareem
- Subjects
General Computer Science ,General Mathematics ,Maximum likelihood ,General Physics and Astronomy ,General Chemistry ,01 natural sciences ,Agricultural and Biological Sciences (miscellaneous) ,General Biochemistry, Genetics and Molecular Biology ,010104 statistics & probability ,03 medical and health sciences ,0302 clinical medicine ,030220 oncology & carcinogenesis ,Botany ,Burr-XII failure model, Maximum likelihood estimator, Moments estimator, Percentile estimator ,lcsh:Q ,0101 mathematics ,lcsh:Science ,Mathematics - Abstract
This paper deals with defining Burr-XII, and how to obtain its p.d.f., and CDF, since this distribution is one of failure distribution which is compound distribution from two failure models which are Gamma model and weibull model. Some equipment may have many important parts and the probability distributions representing which may be of different types, so found that Burr by its different compound formulas is the best model to be studied, and estimated its parameter to compute the mean time to failure rate. Here Burr-XII rather than other models is consider because it is used to model a wide variety of phenomena including crop prices, household income, option market price distributions, risk and travel time. It has two shape-parameters (α, r) and one scale parameter (λ) which is considered known. So, this paper defines the p.d.f. and CDF and derives its Moments formula about origin, and also derive the Moments estimators of two shapes parameters (α, r) in addition to maximum likelihood estimators as well as percentile estimators, the scale parameter (λ) is not estimated (as it is considered known). The comparison between three methods is done through simulation procedure taking different sample size (n=30, 60, 90) and different sets of initial values for (α, r, λ).It is observed that the moment estimators are the best estimator with percentage (46%) ,(42%) respectively compared with other estimators.
- Published
- 2020