Related papers: On new tests for the Poisson distribution based on…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…
We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained which can be used for parameter estimations and goodness-of-fit testing when adjusting curves…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
Chi-squared tests for lack of fit are traditionally employed to find evidence against a hypothesized model, with the model accepted if the Karl Pearson statistic comparing observed and expected numbers of observations falling within cells…
We propose a new $L^2$-type goodness-of-fit test for the family of beta distributions based on a conditional moment characterisation. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a…
The paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…
We consider the error distribution in functional linear models with scalar response and functional covariate. Different asymptotic expansions of the empirical distribution function and the empirical characteristic function based on…
Thousands of experiments are analyzed and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived -- somewhat naively -- as saturated, several misconceptions still…
We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical…
A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the…
We propose new goodness-of-fit tests for the Pareto type I distribution. These tests are based on a multiplicative version of the memoryless property which characterises this distribution. We present the results of a Monte Carlo power study…
Gaussian functions are commonly used in different fields, many real signals can be modeled into such form. Research aiming to obtain a precise fitting result for these functions is very meaningful. This manuscript intends to introduce a new…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
We present a new class of multivariate binning-free and nonparametric goodness-of-fit tests. The test quantity \emph{energy} is a function of the distances of observed and simulated observations in the variate space. The simulation follows…
In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution.…