Affiliations: [a] Department of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia | [b] Department of Mathematical Methods in Economics, Plekhanov Russian University of Economics, Moscow, Russia
Corresponding author: Olga Sviridova, %****␣mas-14-mas180453_temp.tex␣Line␣25␣**** Department of Mathematical Methods in Economics, Plekhanov Russian University of Economics, Moscow, Russia. E-mail: [email protected].
Abstract: It is shown that for a small sample size, when the maximum likelihood estimators lose its asymptotic properties, a more accurate point and interval estimation of the Poisson distribution parameter requires a direct investigation of the properties of the normalized likelihood function. Alternative point and interval estimates of the distribution parameter are obtained.
Keywords: Normalized likelihood function, Poisson type distribution, point estimate, confidence interval