Maximum Likelihood Method: An Alternative To Ordinary Least Square Method In Estimating The Parameters Of Simple Weibull Distribution Using Large Samples Of Type-I Censored Observation. (Published)
This study is concerned with two-parameter Weibull distribution which is very important in life testing and reliability analysis. Two methods viz: maximum likelihood estimation (MLE) and Ordinary Least Squares (OLS) are good alternatives in estimating the parameters of a simple Weibull distribution as the sample sizes increases. These estimators are derived for Random Type-I censored samples. These methods were compared by looking at their standard errors through simulation study with sample sizes of 100, 300, 500 and 1000. It was observed that MLE stands out when estimating the parameters of the Weibull distribution as the sample size increases compared to the OLSM. We also noted that both OLSM and MLE provides asymptotically normally distributed estimator.
Keywords: Maximum Likelihood Estimation, Ordinary least square estimation, Random Type-I censoring, simulation study and Weibull distribution.
Maximum Likelihood Method: An Alternative To Ordinary Least Square Method In Estimating The Parameters Of Simple Weibull Distribution Using Large Samples Of Type-I Censored Observation (Published)
This study is concerned with two-parameter Weibull distribution which is very important in life testing and reliability analysis. Two methods viz: maximum likelihood estimation (MLE) and Ordinary Least Squares (OLS) are good alternatives in estimating the parameters of a simple Weibull distribution as the sample sizes increases. These estimators are derived for Random Type-I censored samples. These methods were compared by looking at their standard errors through simulation study with sample sizes of 100, 300, 500 and 1000. It was observed that MLE stands out when estimating the parameters of the Weibull distribution as the sample size increases compared to the OLSM. We also noted that both OLSM and MLE provides asymptotically normally distributed estimator.
Keywords: Maximum Likelihood Estimation, Ordinary least square estimation, Random Type-I censoring, simulation study and Weibull distribution.
ESTIMATION OF EXTREME VALUE AT RISK IN RWANDA EXCHANGE RATE (Published)
Estimating the probability of rare and extreme events is a crucial issue in the risk estimation of exchange rate returns. Extreme Value Theory (EVT) is a well-developed theory in the field of probability that studies the distribution of extreme realizations of a given distribution function, or of a stochastic process, satisfying certain assumptions. This work has fitted the Generalized Pareto Distribution (GPD) to the excess returns assuming the residuals are independent and identically distributed. The results are used to estimate extreme Value at Risk (VaR) in Rwanda exchange rate process.
Keywords: Confidence intervals, EVT approach, Exchange Rate, Generalized Pareto Distribution, Maximum Likelihood Estimation, Value at Risk