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Some applications of probability generating function based methods to statistical estimation

100%

Esquível M.

Discussiones Mathematicae Probability and Statistics

2009

tom 29

nr 2

131-153

After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure by simulation and we prove the consistency of the estimator.

Binomial ARMA count series from renewal processes

63%

Koshkin S., Cui Y.

Discussiones Mathematicae Probability and Statistics

2012

tom 32

nr 1-2

5-16

This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration.

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2 Discussiones Mathematicae Probability and Statistics

1 Cui Y.

1 Esquível M.

1 Koshkin S.

1 2012

1 2009

Wyniki wyszukiwania

Some applications of probability generating function based methods to statistical estimation

Binomial ARMA count series from renewal processes