An estimator is said to be of orders0 if its bias has magnitude n−s, where n is the sample size. We give delta estimators and jackknife estimators of order four for smooth functions of the parameters of a multinomial distribution. An unbiased estimator is given for its density function. We...

Control charts, known for more than 80 years, have been important tools for business and industrial manufactures. Among many different types of control charts, the attribute control chart (np-chart or p-chart) is one of the most popular methods to monitor the number of observed defects in...

This paper concentrates on negatively skewed one-sided distributions as an explanation of the occurence of positive (negative) skewness in the case of stochastic production (cost) frontier analysis. It takes as example the binomial distribution that can have negative or positive skew and derives...

In order to approach a distribution by means of simulation it is necessary to determine a number of replications. The accuracy with which the distribution is calculated will rely on this number of replications. In this work, a relationship between the number of replications and the accuracy of...

This paper uses the setting of a volleyball game and an exotic sports betting on the point difference of volleyball games to test whether people correctly understand the probabilities related to outcomes of a process which follows a binomial distribution. We find that people consistently...

Uncertainty about the riskiness of new financial products was an important factor behind the U.S. credit crisis. We show that a boom-bust cycle in debt, asset prices and consumption characterizes the equilibrium dynamics of a model with a collateral constraint in which agents learn "by...

Data envelopment analysis (DEA) is a deterministic econometric model for calculating efficiency by using data from an observed set of decision-making units (DMUs). We propose a method for calculating the distribution of efficiency scores. Our framework relies on estimating data from an...

Two interesting results encountered in the literature concerning the Poisson and the negative binomial distributions are due to MORAN (1952) and PATIL & SESHADRI (1964), respectively. MORAN's result provided a fundamental property of the Poisson distribution. Roughly speaking, he has shown that...

Let X, Y be two discrete random variables with finite support and X≥Y. Suppose that the conditional distribution of Y given X can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution of X (and hence the joint distribution of (X,...