Purpose – The purchase distribution of consumer packaged goods has been extensively modelled by the negative binomial distribution (NBD). As the characteristics of packaged goods differ from those of subscription services, the latter may be a boundary condition for NBD. In this study, the...

Purpose – The purpose of this paper is to introduce the zero‐modified distributions in the calculation of operational value‐at‐risk. Design/methodology/approach – This kind of distributions is preferred when excess of zeroes is observed. In operational risk, this phenomenon may be due...

Coherent-ambiguity aversion is defined within the (Klibanoff et al., Econometrica 73:1849–1892, <CitationRef CitationID="CR40">2005</CitationRef>) smooth-ambiguity model (henceforth KMM) as the combination of choice-ambiguity and value-ambiguity aversion. Five ambiguous decision tasks are analyzed theoretically, where an individual faces...</citationref>

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...

Recursive formulas are provided for computing probabilities of a multinomial distribution. Firstly, a recursive formula is provided for computing rectangular probabilities which include the cumulative distribution function as a special case. These rectangular probabilities can be used to provide...

We first show that any 1−α bootstrap percentile confidence interval for a proportion based on a binomial random variable has an infimum coverage probability zero for any sample size. This result is then extended to intervals for the difference, the relative risk and the odds ratio of two...

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...

It is widely recognized that measurement errors often exist in practice and may considerably affect the performance of control charts in some cases. Measurement error variability has uncertainty which may be originated from several sources. Recently, Chakraborty and Khurshid [3] studied the...

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded...