Inferences for the ratio: Fieller’s interval,log ratio,and large sample based confidence intervals

In sample surveys and many other areas of application, the ratio of variables is often of great importance. This often occurs when one variable is available at the population level while another variable of interest is available for sample data only. In this case, using the sample ratio, we can often gather valuable information on the variable of interest for the unsampled observations. In many other studies, the ratio itself is of interest, for example when estimating proportions from a random number of observations. In this note we compare three confidence intervals for the population ratio: A large sample interval, a log based version of the large sample interval, and Fieller’s interval. This is done through data analysis and through a small simulation experiment. The Fieller method has often been proposed as a superior interval for small sample sizes. We show through a data example and simulation experiments that Fieller’s method often gives nonsensical and uninformative intervals when the observations are noisy relative to the mean of the data. The large sample interval does not similarly suffer and thus can be a more reliable method for small and large samples.     

An asymptotic distribution of wright’s process capability index sensitive to skewness

In a recent paper (J. Statist. Comput. Simul., 1995, Vol.53, pp. 195–203) P. A. Wright proposed a new process capability index C_s which generalizes the Pearn-Kotz-Johnson’s index C_pmk by taking into account the skewness (in addition to deviation of the mean from tliCrntarget already incorporated in C_pmk ). The purpose of this article is to study the consistency and asymptotics of an estimate ?_s of C_s The asymptotic distribution provides an insight into some desirable properties of the estimate which are not apparent from its original definition     

A multivariate test for detecting fraud based on Benford’s law,with application to music streaming data

Statistical Methods & Applications - Benford’s law became a prevalent concept for fraud and anomaly detection. It examines the frequencies of the leading digits of numbers in a collection...     

Modelling and research on manufacturer’s capacity of remanufacturing and recycling in closed-loop supply chain

This paper introduces and analyses the present situation of the electronic waste recycling at home and abroad. Involving manufacturers in the recycling process of supply chain as the dominant party and establishing the closed-loop supply chain system structure model of the waste electronic products recycling, the effects of remanufacturing capacity and recycling coefficient on the closed-loop supply chain recycling network are analysed by using system dynamics method. The simulation results show that, compared with the traditional supply chain, the total revenue of the supply chain under the recycling mode dominated by manufacturers has improved, that the increase of the remanufacturing capacity has promoted the growth of the electronic product's sales rate, which reaches a equilibrium when remanufacturing capacity is set as 0.36, and that the recycling efficiency of e-waste has improved significantly as the e-waste recycling coefficient constantly increased.     

An accurate,tractable, and analytically integrable polynomial expansion of the skewed Student’s t-distribution

An integrable polynomial expansion is derived for the skewed Student’s t-distribution. Analytic integration of the density function results in a polynomial expression for the cumulative distribution function too, which is easily manageable from a numerical and mathematical point of view and enables computing quantiles with minimum numerical effort.     

On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum–Saunders distribution based on Type-I,Type-II and hybrid censored samples

The Birnbaum–Saunders (BS) distribution is a positively skewed distribution and is a common model for analysing lifetime data. In this paper, we discuss the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of BS distribution based on Type-I, Type-II and hybrid censored samples. The line of proof is based on the monotonicity property of the likelihood function. We then describe the numerical iterative procedure for determining the MLEs of the parameters, and point out briefly some recently developed simple methods of estimation in the case of Type-II censoring. Some graphical illustrations of the approach are given for three real data from the reliability literature. Finally, for illustrative purpose, we also present an example in which the MLEs do not exist.