Journal ArticleDOI
Estimation of Probability Density Function based on Random Number of Observations with Applications
TLDR
This paper deals with the problem of estimating the probability density function (p.d.f.) of a random variable (r.v.) based on random number of observations and investigates the asymptotic properties of a class of estimates j.f (x) of the p.f. (x), which is defined by Parzen (1962).Abstract:
In this paper we deal with the problem of estimating the probability density function (p.d.f.) of a random variable (r.v.) based on random number of observations. Parzen (1962) has investigated the asymptotic properties of a class of estimates j. (x) of the p.d.f. f(x) of a r.v. X based on n independent observations X1, ..., Xn. The estimate jf (x) is defined byread more
Citations
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Journal ArticleDOI
On sequential density estimation
TL;DR: In this article, the authors consider the problem of estimating a density function at a point x 0 which may be known or unknown, and show that for two classes of density estimators f n, namely the kernel estimates and a recursive modification of these, they are asymptotically normally distributed when properly normed.
Journal ArticleDOI
Bayes Prediction in a Pareto Lifetime Model With Random Sample Size
TL;DR: In this article, the problem of predicting the future ordered observations in a sample of size n from a Pareto distribution where the first r ordered observations have been observed is addressed, assuming that the sample size n is a random variable having a Poisson or binomial distribution.
Journal ArticleDOI
Sequential and recursive estimators of the probability density
TL;DR: A survey over the field of recursive and sequential density estimation summarizes results for kernel estimators can be found in this article, where the problems of consistency in the quadratic mean and almost surely are considered.
Journal ArticleDOI
Optimal random sample size based on Bayesian prediction of exponential lifetime and application to real data
TL;DR: This paper responds to the problem of Bayesian predicting future observations from an exponential distribution based on an observed sample, when the information sample size is fixed as well as a random variable, by considering two criteria, total cost of experiment and mean squared prediction error in prediction problem.
References
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Journal ArticleDOI
On Estimation of a Probability Density Function and Mode
TL;DR: In this paper, the problem of the estimation of a probability density function and of determining the mode of the probability function is discussed. Only estimates which are consistent and asymptotically normal are constructed.
Journal ArticleDOI
Large-sample theory of sequential estimation
TL;DR: A proposition is established that fixed-sample-size formulae might be valid generally for sequential sampling, provided the sample size was large, and some situations in which the uniform continuity condition postulated in Theorems 1 and 2 is satisfied.
Journal ArticleDOI
On the Estimation of the Probability Density, I
G. S. Watson,M. R. Leadbetter +1 more
TL;DR: In this paper, the properties of such estimators are discussed on the basis of their mean integrated square errors (M.I.S.E), and the corresponding development for discrete distributions is sketched and examples are given in both continuous and discrete cases.