Martin Fox

Estimation of the Parameter n in the Binomial Distribution

Let Xi, … Xr, be independent B(n,p) random variables. In this paper n is estimated with known p. The MLE is developed and shown to be consistent in a relative sense and asymptotically normal. Motivated by Yi = Xi/q we consider Y1, … Yr independent N(μ,μ) and examine three estimates of μ; (i) the MVUE, (ii) the MLE, and (iii) . These are shown to be asymptotically equivalent.

Sample size choice : charts for experiments with linear models

A guide to testing statistical hypotheses for readers familiar with the Neyman-Pearson theory of hypothesis testing including the notion of power, the general linear hypothesis (multiple regression) problem, and the special case of analysis of variance. The second edition (date of first not mentione

Probability : the mathematics of uncertainty

Of course, from childhood to forever, we are always thought to love reading. It is not only reading the lesson book but also reading everything good is the choice of getting new inspirations. Religion, sciences, politics, social, literature, and fictions will enrich you for not only one aspect. Having more aspects to know and understand will lead you become someone more precious. Yea, becoming precious can be situated with the presentation of how your knowledge much.

Adaptive estimation of a function of a mean vector

A sample is taken from some r-dimensional distribution with mean vector [mu] and the value of [theta] = P([mu]) is to be estimated. Here P is a polynomial. An initial sample of size n1 is taken and all components are observed. Assume that, after the initial sample, the remaining sampling budget is C and the cost of each new vector taken is c0 with an additional cost cj if component j is observed. A subset D [not equal to] O of {1,h.,r} is selected and a second sample of size n2 is taken in which only those components with index j [set membership, variant] D are observed. It is desired to select D to minimize the MSE of the estimator where the components of are the sample means of observed components. Consider the case P([mu]) = [product operator]j-1r [mu]j. Assume that E([product operator]j=1rXj2)

Three Simple Inductive Proofs in Probability and Statistics

Abstract Elementary inductive proofs are presented for the binomial approximation to the hypergeometric distribution, the density of an order statistic, and the distribution of when X 1, ···, X n are a sample from N (μ, 1).