Abstract In this paper, the estimation of R=Pr(Y < Y), when X and Y are two generalized inverted exponential distributions with different parameters is considered. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. Exact and asymptotic confidence intervals of R are constructed using both exact and asymptotic distributions. Assuming that the common scale pa...

when a change occurs in a process, one expects to receive a signal from a control chart as quickly as possible. upon the receipt of signal from the control chart a search for identifying the source of disturbance begins. however, searching for assignable cause around the signal time, due to the fact that the disturbance may have manifested itself into the rocess sometimes back, may not always l...

Counts of a specific characteristic were obtained within regions defined on an object that was manufactured in proprietary setting. The count altered during production and resulted misaligned or overlapping data. A closed-formula maximum likelihood estimator (MLE) the new region means is derived using all available data independent Poisson model. MLE shown to be preferable estimators constructe...

This paper provides closed-form likelihood approximations for multivariate jump-diffusion processes widely used in finance. For a fixed order of approximation, the maximum-likelihood estimator (MLE) computed from this approximate likelihood achieves the asymptotic efficiency of the true yet uncomputable MLE as the sampling interval shrinks. This method is used to uncover the realignment probabi...

We describe a novel algorithm called k-Maximum Likelihood Estimator (k-MLE) for learning finite statistical mixtures of exponential families relying on Hartigan’s k-means swap clustering method. To illustrate this versatile Hartigan k-MLE technique, we consider the exponential family of Wishart distributions and show how to learn their mixtures. First, given a set of symmetric positive definite...

We consider a particular maximum likelihood estimator (MLE) and a computationally-intensive Bayesian method for differentially private estimation of the linear mixed-effects model (LMM) with normal random errors. The LMM is important because it is used in small area estimation and detailed industry tabulations that present significant challenges for confidentiality protection of the underlying ...

Estimating the cardinality (i.e. number of distinct elements) of an arbitrary set expression defined over multiple distributed streams is one of the most fundamental queries of interest. Earlier methods based on probabilistic sketches have focused mostly on the sketching algorithms. However, the estimators do not fully utilize the information in the sketches and thus are not statistically effic...

Abstract A Fibonacci-type probability distribution provides the probabilistic models for establishing stopping rules associated with number of consecutive successes. It can be interpreted as a generalized version geometric distribution. In this article, after revisiting to explore its definition, moments and properties, we proposed numerical methods obtain two estimators success probability: me...

When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to good approximation, normally distributed. But, when support boundaries are functions of parameter, finding approximation for sampling distribution MLE (needed construct an accurate confidence interval parameter’s true value) may get very challenging. We demonstrate...