![]() ![]() The variance for truncated geometric distribution is: In this paper, we derived the second moment further.įor the second moment and by second differentiation we have, Thus, is the sample mean, as demonstrated by. Therefore we intend to derive the distributional properties of our estimates by looking at the expectation and variance of truncated geometric distribution. These are the probabilities of truncated geometric distribution with parameter P and N terms. Hence, the probability density function is: We shall introduce a truncated form of the geometric distribution and then demonstrate that it is suitable model for a probability distribution. and N terms, when it has the probability distribution. Įstimating the Parameter of Truncated Geometric Distribution.Ī random variable X may be defined to have a truncated geometric distribution, with parameter p. The truncation is more than just theoretical interest as a number of applications have been reported in. ![]() On this note we propose a stationary bootstrap method generated by resampling blocks of random size, where the length of each block has a “truncated geometric distribution”. ![]() Their sampling procedure have been generalized by by resampling “blocks of blocks” of observations for the stationary time series process. Recently, and have independently introduced non-parametric versions of the bootstrap that are applicable to weakly dependent stationary observations. Īn excellent introduction to the bootstrap may be found in the work of. The bootstrap methods have and will continue to have a profound influence throughout science as the availability of fast, inexpensive computing has enhanced our abilities to make valid statistical inferences about the world without the need for using unrealistic or unverifiable assumptions. The Bootstrap approach, as initiated by, avoids having to derive formulas via different analytical arguments by taking advantage of fast computers. Bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis. ![]() Bootstrap method relies on using an original sample or some part of it, such as residuals as an artificial population from which to randomly resample. The heart of the bootstrap is not simply computer simulation, and bootstrapping is not perfectly synonymous with Monte Carlo. The second part of the paper uses the distribution to developed bootstrap algorithm for stationary time series process to overcome the difficulties of moving block scheme and geometric Bootstrap scheme of in determining probability p and block size b respectively. The first part of the present paper shows how to estimate the parameter of truncated geometric distribution as a true probability model, by method of moment. also treated the truncated binomial and negative binomial distribution and truncated Poisson distribution and has shown how to estimate the parameter of distributions. has treated the truncated binomial distribution. Several studies have been made of truncated distribution. Keywords:Truncated Geometric Bootstrap Method, Stationary Process, Moving Block and Geometric Stationary Bootstrap Method The mean and variance were estimated for the truncated geometric distribution and the bootstrap algorithm developed based on the proposed probability model. The method was able to determine the block sizes b and probability p attached to its random selections. This probability model was used in resampling blocks of random length, where the length of each blocks has a truncated geometric distribution. We estimate the parameters of a geometric distribution which has been truncated as a probability model for the bootstrap algorithm. This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. Received 28 April 2014 revised accepted 10 June 2014 This work is licensed under the Creative Commons Attribution International License (CC BY). Department of Mathematical Science, Olabisi Onabanjo University, Ago-Iwoye, NigeriaĮmail: © 2014 by author and Scientific Research Publishing Inc. ![]()
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