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In this paper we study the performance of the least square method, the weighted least square method, the maximum likelihood method and the method of moments for estimating the Weibull distribution parameters. The comparison is based on the Monte Carlo simulation, the methods are compared in terms of the root mean square error and sample size n. The comparison shows that the maximum likelihood method and the method of moments provide similar estimates. We recommend the maximum likelihood method to estimate the Weibull distribution parameters due to its good properties. For very small sample sizes we recommend the weighted least square method.

In this paper we study new distribution called transmuted Weibull distribution. Some properties of this distribution are described. The usefulness of the distribution for modelling data is illustrated using real data set.

The paper deals with systems of linear differential equations with coefficients depending on the Markov process. Equations for particular density and the moment equations for given systems are derived and used in the investigation of solvability of initial problems and stability. Results are illustrated by examples. MSC: 34K50; 60H10; 60H30; 65C30

The paper deals with a system of difference equations, where coefficients depend on Markov chains. The functional equations for particular density and the moment equations for the system are derived and used in the investigation of solvability and stability. An application of the results is shown how to solve various economic problems. c 2013 Mathematical Institute, Slovak Academy of Sciences. 2010 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: 34K50, 60H10, 60H30, 65C30. K e y w o r d s: stochastic systems, Markov chain, moment equations, stability.