Parameter Estimation of Bernoulli Distribution using Maximum Likelihood and Bayesian Methods

Nurmaita Hamsyiah, Nisa Nisa, Warsono Warsono

Abstract


The term parameter estimation refers to the process of using sample data to estimate the parameters of theselected distribution.There are several methodsthat can be used to estimate distributionparameter(s).In thispaper,the maximum likelihood andBayesian methodsare usedfor estimating parameter ofBernoulli distribution,i.e. , which isdefined asthe probability of success event for two possible outcomes.The maximum likelihood andBayesian estimators of Bernoulli parameter are derived,for the Bayesian estimator the Beta prior is used. Theanalytical calculation shows that maximum likelihood estimator is unbiased while Bayesian estimator isasymptotically unbiased. However, empirical analysis by Monte Carlo simulation shows that the mean squareerrors (MSE) of the Bayesian estimatorare smaller than maximum likelihood estimator for large sample sizes.

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