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1

Nonparametric Versus Parametric Reasoning Based on 22 Contingency Tables

Sulewski P.

Computational Methods in Science and Technology

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2018

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Vol. 24, No. 2

143--153

EN

This paper proposes scenarios of generating contingency tables (CTs) with the probability flow parameter (PFP). It also defines measures of untruthfulness of H0 that involve PFP for all proposed scenarios. This paper is an attempt to replace a nonparametric statistical inference method by the parametric one. The paper applies the maximum likelihood method to estimate PFP and presents instructions to generate CTs by means of the bar method. The Monte Carlo method is used to carry out computer simulations.

2

Record-based inference and associated cost analysis for the Weibull distribution

Doostparast M.

Control and Cybernetics

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2015

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Vol. 44, no. 1

163--177

EN

In statistical process control, record schemes are used to reduce the total time on test for the inspection inquiry. In these schemes, units are examined sequentially and successive minimum values are recorded. On the basis of record data, Samaniego and Whitaker (1986) obtained the maximum likelihood (ML) estimate of the mean for an exponential distribution. Since the two parameter Weibull model, as an extension of the exponential distribution, has a wide range of application, Hoinkes and Padgett (1994) derived the record-based ML estimators for the parameters of interest in this model. This paper shows that the ML estimates of the Weibull parameters do not always exist for the basis of records. Thus, a new scheme is proposed, in which the ML estimates of the parameters always exist. An analytic cost-based comparison between the usual and the New scheme is also carried out. Finally, some concluding remarks and open problems are formulated.

3

Lifetime distributions with wave-like bathtub hazard

Guo R., Thiart C., Cui Y., Guo D.

Journal of Polish Safety and Reliability Association

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2011

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Vol. 2, No. 1

115--122

EN

In this paper, we argue the necessity of dealing with lifetime distributions with wave-like bathtub hazard function. Four classes of wave-like bathtub hazards are investigated. For preparing maximum likelihood estimation of the hazard parameters, the first-order and second-order partial derivatives are derived.

4

Monte Carlo methods of estimating transition density and likelihood function of diffusion processes

Borkowski P., Mielniczuk J.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2009

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Nr 1013

1-23

EN

The properties of various Monte Carlo schemes for estimating transition density of discretely observed diffusion processes are discussed. The considered methods include various importance samplers with weighing distribution taking into account observed trajectory of the process. They are then used to evaluate simulated likelihood function and maximum likelihood estimators.

PL

W pracy rozważane są różne warianty metody Monte Carlo dla estymacji gęstości prawdopodobieństwa przejścia na podstawie procesu dyfuzji obserwowanego w dyskretnych momentach czasowych. W szczególności bada się ważoną metodę Monte Carlo, w której stosowane wagi zależą od obserwowanej trajektorii procesu. Estymatory gęstości przejścia są następnie wykorzystane do estymacji funkcji wiarogodności i estymatorów największej wiarogodności.

5

Calculation of Functionals Based on Large Dimension Matrixes in Maximal Likelihood Problems

Medvedev G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2005

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Vol. 10

95--105

EN

The problem of the likelihood function calculation is examined AT parameter estimation of the stochastic process describing the change of interest rates in the financial market. Such a problem arises, when it is supposed that the process is not a usual diffusion process, but posesses continuous derivatives. In this case the increments of the proccess become correlated, and for the likelihood function evaluation it is necessary to invert a matrix of the high order equal to sample size. As it is known the calculation of reciprocal matrixes of the high order either is impossible or results in essential error of calculation. In this paper the way to avoid this difficulty is offered.