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In this paper we present an alternative representation of the Negative Binomial--Lindley distribution recently proposed by Zamani and Ismail (2010) which shows some advantages over the latter model. This new formulation provides a tractable…
The Box--Cox transformation model has been widely applied for many years. The parametric version of this model assumes that the random error follows a parametric distribution, say the normal distribution, and estimates the model parameters…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
As a classic parameter from the binomial distribution, the binomial proportion has been well studied in the literature owing to its wide range of applications. In contrast, the reciprocal of the binomial proportion, also known as the…
We consider the complex data modeling problem motivated by the zero-inflated and overdispersed data from microbiome studies. Analyzing how microbiome abundance is associated with human biological features, such as BMI, is of great…
The present paper makes a study on Partition sort algorithm for negative binomial inputs. Comparing the results with those for binomial inputs in our previous work, we find that this algorithm is sensitive to parameters of both…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
Nonlinear Mixed effects models are hidden variables models that are widely used in many fields such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters…
Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in the model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the overdispersion parameter…
Likelihood-free methods are useful for parameter estimation of complex models with intractable likelihood functions for which it is easy to simulate data. Such models are prevalent in many disciplines including genetics, biology, ecology…
Comparison of two univariate distributions based on independent samples from them is a fundamental problem in statistics, with applications in a wide variety of scientific disciplines. In many situations, we might hypothesize that the two…
There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…
The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…
Single index linear models for binary response with random coefficients have been extensively employed in many econometric settings under various parametric specifications of the distribution of the random coefficients. Nonparametric…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
The reproductive habits of helminths are important for the study of the dynamics of their transmission. For populations of parasites distributed by Poisson or negative binomial models, these habits have already been studied. However, there…
This work presents a construction of stationary Markov models with negative-binomial marginal distributions. A simple closed form expression for the corresponding transition probabilities is given, linking the proposal to well-known classes…