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Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers

Kuo-Hsiung Wang, Sheau-Chyi Chen, Jau-Chuan Ke (2010)

RAIRO - Operations Research

This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability (1 - b). We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heterogeneous servers in the literature. We also develop the confidence interval formula for the parameter...

Mean square error of the estimator of the conditional hazard function

Abbes Rabhi, Samir Benaissa, El Hadj Hamel, Boubaker Mechab (2013)

Applicationes Mathematicae

This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.

Measuring association via lack of co-monotonicity: the LOC index and a problem of educational assessment

Danang Teguh Qoyyimi, Ricardas Zitikis (2015)

Dependence Modeling

Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education,which is of our primary interest in this paper. Given, for example, student marks on several study subjects, we may for a number of reasons be interested in measuring the lack of comonotonicity (LOC) between the marks, which rarely follow monotone, let alone linear, patterns. For this purpose, in this paperwe explore a novel approach based on a LOCindex,which is...

Median for metric spaces

Nacereddine Belili, Henri Heinich (2001)

Applicationes Mathematicae

We consider a Köthe space ( , | | · | | ) of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that | | d ( X , Y ) | | ≤ | | d ( X , Z ) | | for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications....

Medida de asociación propia entre variables aleatorias discretas.

María del Carmen Carollo Limeres (1984)

Trabajos de Estadística e Investigación Operativa

En este trabajo estudiamos la asociación entre dos variables aleatorias discretas (no cardinales) definiendo una nueva medida [de] asociación, la cual está basada en la velocidad de convergencia del vector de probabilidad correspondiente a la cadena de Markov asociada a la distribución de probabilidad conjunta de las variables en estudio. Ponemos especial énfasis en el estudio muestral y propiedades de los estimadores de dicha medida, calculando sus distribuciones asintóticas bajo el muestreo multinomial...

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