scholarly journals Wrapped Zero-inflated Poisson Distribution and Its Properties

2015 ◽  
Vol 5 (1) ◽  
pp. 111
Author(s):  
Anita Brobbey ◽  
Aerambamoorthy Thavaneswaran ◽  
Saumen Mandal
Keyword(s):  
Poisson Distribution ◽  
Population Characteristics ◽  
Function Approach ◽  
Characteristic Functions ◽  
Model Parameters ◽  
Stable Processes ◽  
Estimating Function ◽  
Circular Distribution ◽  
Wrapped Distributions ◽  
Trigonometric Moments

Recently, there has been a growing interest in discrete valued wrapped distributions and the trigonometric moments.<br />Characteristic functions of stable processes have been used to study the estimation of the model parameters using<br />estimating function approach (Thavaneswaran et al., 2013). In this paper, we introduce a new discrete circular distribution,<br />the wrapped zero-inflated Poisson distribution and derive its population characteristics.<br /><br />

scholarly journals Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions

2016 ◽  
Vol 5 (3) ◽  
pp. 1 ◽  
Author(s):  
Aerambamoorthy Thavaneswaran ◽  
Saumen Mandal ◽  
Dharini Pathmanathan
Keyword(s):  
Closed Form ◽  
Information Matrix ◽  
Score Function ◽  
Function Approach ◽  
Closed Form Expression ◽  
Characteristic Functions ◽  
Model Parameters ◽  
Estimating Function ◽  
Method Of Moment ◽  
Poisson Distributions

There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

An estimating function approach to linkage heterogeneity

2013 ◽  
Vol 92 (3) ◽  
pp. 413-421
Author(s):  
HE GAO ◽  
YING ZHOU ◽  
WEIJUN MA ◽  
HAIDONG LIU ◽  
LINAN ZHAO
Keyword(s):  
Function Approach ◽  
Estimating Function

scholarly journals Transformation of circular random variables based on circular distribution functions

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5931-5947
Author(s):  
Hatami Mojtaba ◽  
Alamatsaz Hossein
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Real Data ◽  
Random Variable ◽  
Distribution Functions ◽  
Likelihood Method ◽  
Circular Distribution ◽  
Data Set ◽  
Trigonometric Moments ◽  
Von Mises

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

scholarly journals Global sensitivity analysis of parameter uncertainty in landscape evolution models

2018 ◽  
Vol 11 (12) ◽  
pp. 4873-4888 ◽  
Author(s):  
Christopher J. Skinner ◽  
Tom J. Coulthard ◽  
Wolfgang Schwanghart ◽  
Marco J. Van De Wiel ◽  
Greg Hancock
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Landscape Evolution ◽  
Relative Sensitivity ◽  
Function Approach ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Model Function ◽  
Sediment Yields ◽  
Statistical Measures

Abstract. The evaluation and verification of landscape evolution models (LEMs) has long been limited by a lack of suitable observational data and statistical measures which can fully capture the complexity of landscape changes. This lack of data limits the use of objective function based evaluation prolific in other modelling fields, and restricts the application of sensitivity analyses in the models and the consequent assessment of model uncertainties. To overcome this deficiency, a novel model function approach has been developed, with each model function representing an aspect of model behaviour, which allows for the application of sensitivity analyses. The model function approach is used to assess the relative sensitivity of the CAESAR-Lisflood LEM to a set of model parameters by applying the Morris method sensitivity analysis for two contrasting catchments. The test revealed that the model was most sensitive to the choice of the sediment transport formula for both catchments, and that each parameter influenced model behaviours differently, with model functions relating to internal geomorphic changes responding in a different way to those relating to the sediment yields from the catchment outlet. The model functions proved useful for providing a way of evaluating the sensitivity of LEMs in the absence of data and methods for an objective function approach.

scholarly journals A NUMERICAL EXPERIMENT ON MATHEMATICAL MODEL OF FORECASTING THE RESULTS OF KNOWLEDGE TESTING

2011 ◽  
Vol 17 (1) ◽  
pp. 42-61 ◽  
Author(s):  
Natalja Kosareva ◽  
Aleksandras Krylovas
Keyword(s):  
Mathematical Model ◽  
Characteristic Function ◽  
Goodness Of Fit ◽  
Characteristic Functions ◽  
Model Parameters ◽  
Information Function ◽  
Test Information ◽  
Parametric Functions ◽  
Office Rooms ◽  
Test Information Function

In this paper the new approach to the forecasting the results of knowledge testing, proposed earlier by authors, is extended with four classes of parametric functions, the best fitting one from which is selected to approximate item characteristic function. Mathematical model is visualized by two numerical experiments. The first experiment was performed with the purpose to show the procedure of selecting the most appropriate item characteristic function and adjusting the parameters of the model. Goodness-of-fit statistic for detecting misfit of the selected model is calculated. In the second experiment a test of 10 items is constructed for the population with latent ability having normal distribution. Probability distribution of total test result and test information function are calculated when item characteristic functions are selected from four classes of parametric functions. In the next step it is shown how test information function value could be increased by adjusting parameters of item characteristic functions to the observed population. This model could be used not only for knowledge testing but also when solving diagnostic tasks in various fields of human activities. Other advantage of this method is the reduction of resources of testing process by more precise adjustment of the model parameters and decreasing the standard error of measurement of the estimated examinee ability. In the presented example the methodology is applied for solving the problem of microclimate evaluation in office rooms.

scholarly journals Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

2021 ◽  
Vol 10 (3) ◽  
pp. 8
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Oyebimpe Emmanuel Adeniji ◽  
Kayode Balogun
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Maximum Likelihood Method ◽  
Life Time ◽  
Real Data ◽  
Likelihood Method ◽  
Strength Parameter ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

scholarly journals Measurement Invariance of the Flourishing Scale among a Large Sample of Canadian Adolescents

2020 ◽  
Vol 17 (21) ◽  
pp. 7800
Author(s):  
Isabella Romano ◽  
Mark A. Ferro ◽  
Karen A. Patte ◽  
Ed Diener ◽  
Scott T. Leatherdale
Keyword(s):  
Factor Analysis ◽  
Racial Identity ◽  
Secondary School ◽  
Measurement Invariance ◽  
Secondary School Students ◽  
Population Characteristics ◽  
Psychological Wellbeing ◽  
Model Parameters ◽  
School Students ◽  
Confirmatory Factor

Our aim was to examine measurement invariance of the Flourishing Scale (FS)—a concise measure of psychological wellbeing—across two study samples and by population characteristics among Canadian adolescents. Data were retrieved from 74,501 Canadian secondary school students in Year 7 (2018–2019) of the COMPASS Study and from the original validation of the FS (n = 689). We assessed measurement invariance using a confirmatory factor analysis in which increasingly stringent equality constraints were specified for model parameters between the following groups: study sample (i.e., adolescents vs. adults), gender, grade, and ethno-racial identity. In all models, full measurement invariance of the FS across all sub-groups was demonstrated. Our findings support the validity of the FS for measuring psychological wellbeing among Canadian adolescents in secondary school. Observed differences in FS score among subgroups therefore represent true differences in wellbeing rather than artifacts of differential interpretation.

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