The aim of the paper is to construct a model which describes the life expectancy of privet sawfly females (Macrophya punctumalbum L.), including additional information on the number of eggs. The data on life expectancy of females and their fertility were obtained in the course of research on the bionomy of the privet sawfly. A variety of discrete distributions to modelling the lengths of life was provided, namely: the Poisson Distribution, the Negative Binomial Distribution and the Poisson-inverse Gaussian Distribution. The analysis the above distributions were applied along with the GAMLSS (Generalized Additive Models for Location, Scale and Shape) and the resulting models were compared with the use of the Global Deviance criterion, the Akaike information criterion and the Schwarz Bayesian criterion. For the best model the expected value and the standard deviation were defined. The profile deviance plot of this parameters, analysis of the residuals, kernel density and Q-Q plot are presented, too. All analyses were performed in R with the GAMLSS package.

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