Modeling Repeated Count Data: Some Extensions of the Rasch Poisson Counts Model

1995 ◽  
Vol 20 (3) ◽  
pp. 241-258 ◽  
Author(s):  
Marijtje A. J. van Duijn ◽  
Margo G. H. Jansen
Keyword(s):  
Count Data ◽  
Dirichlet Distribution ◽  
Random Variables ◽  
Data Sets ◽  
Unknown Parameters ◽  
Intensity Parameters ◽  
Test Parameters ◽  
Within Subjects ◽  
The Subject ◽  
Poisson Counts

We consider data that can be summarized as an N × K table of counts—for example, test data obtained by administering K tests to N subjects. The cell entries yij are assumed to be conditionally independent Poisson-distributed random variables, given the NK Poisson intensity parameters μij. The Rasch Poisson Counts Model (RPCM) postulates that the intensity parameters are products of test difficulty and subject ability parameters. We expand the RPCM by assuming that the subject parameters are random variables having a common gamma distribution with fixed unknown parameters and that the vectors of test difficulty parameters per subject follow a common Dirichlet distribution with fixed unknown parameters. Further, we show how additional structures can be imposed on the test parameters, modeling a within-subjects design. Methods for testing the fit and estimating the parameters of these models are presented and illustrated with the analysis of two empirical data sets.

scholarly journals Bivariate discrete Nadarajah and Haghighi distribution: Properties and different methods of estimation

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5589-5610
Author(s):  
Sajid Ali ◽  
Muhammad Shafqat ◽  
Ismail Shah ◽  
Sanku Dey
Keyword(s):  
Exponential Distribution ◽  
Count Data ◽  
Discrete Model ◽  
Discrete Data ◽  
Data Sets ◽  
Applied Statistics ◽  
Reliability Engineering ◽  
Unknown Parameters ◽  
Proposed Model ◽  
Better Than

The exponential distribution is commonly used to model different phenomena in statistics and reliability engineering. A new extension of exponential distribution known as the Nadarajah and Haghighi [An extension of the exponential distribution, Statistics: A Journal of Theoretical and Applied Statistics 45 (2011) 543-558.] distribution was introduced in the literature to accommodate the inflation of zero in the data. In practice, however, discrete data are easy to collect as compared to continuous data. Discrete bivariate distributions play important roles in modeling bivariate lifetime count data. Thus focusing on the utility of discrete data, this study presents a new bivariate discrete Nadarajah and Haghighi distribution. We discuss some basic properties of the proposed distribution and study seven different methods of estimation for the unknown parameters to assess the performance of the proposed bivariate discrete model. Two data sets are also analyzed to demonstrate how the proposed model may work in practice. Results show that the proposed model is very flexible and performs better than some of the existing models.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

scholarly journals Methods of Administrative and Legal Protection of Tax Relations: Theoretical and Legal Study

2019 ◽  
Vol 75 (4) ◽  
pp. 53-58
Author(s):  
K. S. Rohozinnikova
Keyword(s):  
Public Administration ◽  
Open Data ◽  
Legal Protection ◽  
Data Sets ◽  
Administrative Services ◽  
The Public ◽  
The Subject ◽  
State Coercion ◽  
The Relationship ◽  
Functional Purpose

The author of the article has provided the results of the analysis of the methods of administrative and legal protection taking into account the changes within the relations between public administration and taxpayers and the course chosen by the state for liberalization of tax relations. The place of the concept of the methods of administrative and legal protection in the term system of the science of administrative law and their dialectical relations with the methods of public administration and administrative activity has been established. The author has indicated generic and specific features of the methods of administrative and legal protection of tax relations, where the latter will depend on the peculiarities of the means and methods of influence used by the public administration for the purpose of exercising security functions. The system of methods of administrative and legal protection of tax relations has been offered to form from three elements: general methods of administrative activity (persuasion and coercion), service tools of influence (provision of administrative services, creation of electronic services and publication of open data sets) and organizational methods. The expediency of distinguishing service means of influence into a separate group of methods of administrative and legal protection has been proved. It is conditioned by their special functional purpose – creation of conditions for independent prevention of possible breach of protected relations by the taxpayer. The role and correlation of persuasion and coercion in the system of methods of administrative and legal protection of tax relations have been clarified. Despite the presented importance of the persuasion within the relationship between the controlling agencies and the taxpayers, it has been stated that state coercion remains the main mean of administrative and legal protection of tax relations. Particular attention has been paid on the need to reconsider the correlation of tax and administrative coercion within tax relations. It has been proved that the basis of their delimitation should be not the branch of legislation, where the authority to apply the appropriate measure is assigned, but the essential criterion and the subject matter of regulation (influence) – relations arising from incomplete calculation and late and incomplete payment of taxes and fees, or relationships related to the organization and enforcement of tax responsibilities and the proper exercise by the supervisory authorities of their powers. It has been emphasized that tax coercion, unlike administrative, performs both punitive and compensatory functions.

Identification of Nonlinear Systems Parameters Using Polyspectral Measurements and Analysis

1995 ◽  
Author(s):  
Muhammad R. Hajj ◽  
Ali H. Nayfeh ◽  
Pavol Popovic
Keyword(s):  
Experimental Study ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Analytical Techniques ◽  
Modal Interactions ◽  
Unknown Parameters ◽  
Nonlinear Parameters ◽  
The Subject ◽  
Beam Frame ◽  
Subharmonic Resonances

Abstract Experimental and analytical techniques that characterize nonlinear modal interactions in structures are used to quantify parameters in representative nonlinear systems. The subject of the experimental study is a three-beam frame. Subharmonic resonances and interaction between widely spaced modes are exploited to determine nonlinear parameters in models that represent these interactions. The phases of the auto-bispectra of the response of this structure appear in the analytical solutions of the representative models. Values of these phases could thus aid in determining other unknown parameters of nonlinear systems.

PASSENGER RESPONSE TIME DATA- SETS FOR LARGE PASSENGER FERRIES AND CRUISE SHIPS DERIVED FROM SEA TRIALS

2021 ◽  
Vol 155 (A2) ◽  
Author(s):  
R Brown ◽  
E R Galea ◽  
S Deere ◽  
L Filippidis
Keyword(s):  
Response Time ◽  
Research Group ◽  
Data Sets ◽  
Time Data ◽  
Evacuation Time ◽  
The Public ◽  
Cruise Ships ◽  
Passenger Ships ◽  
Unique Nature ◽  
The Subject

The paper consists of 27 figures; numerous equations and 12 notes/ references, many of which are written by the authors of this paper. Whilst this may indicate a lack of “reading around the subject” it also indicates the unique nature of the topic and that little exists at present in the public domain about this topic. Indeed the authors and the research group they represent are the main contributors to the IMOs discussions and circulars on this subject. Given that background the paper is very detailed and consists of comparisons between the evacuation times of 3 passenger ships, 2 being Ro-Pax vessels and 1 a cruise liner. On board evacuation time statistics have been gathered from significant populations enabling the authors to draw significant conclusions relating to evacuation times in the presented scenarios. The paper is therefore a useful addition to the debates on this subject which is of major relevance to the understanding of evacuation times in passenger vessels. Data and research in this area is difficult to obtain thus the authors should be congratulated for their work.

Direct derivation (DD) of weight fractions of individual crystalline phases from observed intensities and chemical composition data: incorporation of the DD method into the whole-powder-pattern fitting procedure

2018 ◽  
Vol 51 (2) ◽  
pp. 446-455 ◽  
Author(s):  
Hideo Toraya
Keyword(s):  
Chemical Composition ◽  
Diffraction Pattern ◽  
Scale Factor ◽  
Powder Pattern ◽  
Data Sets ◽  
Crystalline Phases ◽  
Composition Data ◽  
Intensity Parameters ◽  
Diffraction Patterns ◽  
Integrated Intensities

A formula for quantitative phase analysis (QPA), called the intensity–composition (IC) formula, can be used for deriving weight fractions of individual crystalline phases in a mixture from sets of observed integrated intensities, measured in a wide 2θ range, with chemical composition data [Toraya (2016).J. Appl. Cryst.49, 1508–1516; Toraya (2017).J. Appl. Cryst.50, 820–829]. In this study, the IC formula has been incorporated into the whole-powder-pattern fitting (WPPF) procedure to conduct QPA. The fitting function for calculating the profile intensity at each step of the scattering angle consists of three sub-functions that represent the individual component diffraction patterns. The first sub-function calculates the diffraction pattern using a set of integrated intensities, the parameter values of which are determined by the least-squares fitting of the whole-powder pattern as is usually done by the whole-powder-pattern decomposition (WPPD) method. The second sub-function uses a set of integrated intensity parameters, which are preliminarily prepared by WPPD or may be calculated from a crystal structure model. These intensity parameters, multiplied by a scale factor, are fixed at their original values while the scale factor is adjusted in WPPF. The third sub-function uses an observed or calculated diffraction pattern multiplied by a scale factor. This diffraction pattern can be fitted directly by adjusting the scale factor. Therefore, one can fit patterns consisting of heavily broadened and degraded diffraction lines, like those of clay minerals, without being concerned with the problem of peak overlap in decomposing the diffraction pattern. The IC formula uses the total sums of the intensities under the diffraction patterns of individual phases as observed data sets; therefore, it can equally treat these intensity data sets irrespective of differences in the profile models used by the three sub-functions. The three sub-functions can arbitrarily be chosen and linearly combined, and then they can simultaneously be fitted to the observed diffraction pattern of a target mixture. The capability of the above method has been demonstrated with QPA of mixtures consisting of α-quartz, albite and kaolinite. Theories of currently used QPA techniques are reviewed from a viewpoint of the present theory and they can be interpreted as being based on the same principle, whereby the total observed intensities of individual phases are divided by the standard reference intensity per unit weight.

Muscles versus bones: catfishes as a case study for a discussion on the relative contribution of myological and osteological features in phylogenetic reconstructions

2004 ◽  
Vol 54 (4) ◽  
pp. 373-391 ◽  
Author(s):  
Rui Diogo
Keyword(s):  
Morphological Variation ◽  
Phylogenetic Trees ◽  
High Reliability ◽  
Phylogenetic Analyses ◽  
Data Sets ◽  
Large Set ◽  
Relative Contribution ◽  
Phylogenetic Reconstructions ◽  
The Subject

AbstractThe levels of homoplasy and phylogenetic reliability of different types of data sets have since long intrigued evolutionary scientists. This paper provides, to the author's knowledge, the first assessment of the relative contribution of a large set of myological and osteological characters in simultaneous phylogenetic analyses. The biological taxon used as a case study for this comparison was the highly diverse and cosmopolitan teleost Siluriformes (catfishes) which, with 34 families, about 437 genera and more than 2700 species, represents about one third of all freshwater fishes and one of the most diverse vertebrate groups. Such a direct comparison of the relative contribution of these two types of data sets has the advantage that the homoplasy levels and the phylogenetic trees being compared refer to the same group and, more importantly, to the very same terminal taxa. The overall analysis of the results presented in this work seems to indicate that: (1) osteological structures display a greater morphological variation than myological ones; (2) this difference (which is very likely overenhanced by the fact that the phylogenetic variation of osteological structures has historically been the subject of many more studies and descriptions than myological ones) is particularly notable in small taxa, such as genera or species; (3) myological characters provide, however, a high proportion of informative characters for disclosing the relationships between larger taxa, and, thus, for disclosing the phylogeny of the higher clades in which these taxa are included. These results raise some puzzling, general questions. For instance, what are the reasons for the seemingly greater morphological variation of osteological structures? And why is this greater morphological variation of osteological structures in relation to myological structures particularly pronounced in low ranking taxa? Does natural selection eventually act, in certain cases, more on bones than on muscles? Is the development of myological structures eventually more constrained than that of osteological features? What explains the apparently high reliability of muscular characters to disclose the higher-level phylogeny of higher taxa? More direct comparisons, either of other major groups of teleosts or of vertebrates in general, are clearly needed to infer if the patterns found in the direct comparison of this work correspond to a more general phylogenetic pattern, or instead refer to a particular situation found in the order Siluriformes.

Simulation of Laboratory Jets and Full Scale Exhaust Plumes (Keynote Paper)

2003 ◽  
Author(s):  
Sanford M. Dash
Keyword(s):  
High Speed ◽  
Scale Up ◽  
Turbulence Models ◽  
Operating Conditions ◽  
Data Sets ◽  
Fighter Aircraft ◽  
The Real ◽  
Exhaust Plumes ◽  
Rans Turbulence Models ◽  
The Subject

Recent activities at CRAFT Tech related to the simulation of high speed laboratory jets, their control via passive actuation, and the scale-up and revisions required for real engines and operation at flight are discussed. We focus on aircraft applications related to jet noise reduction with activities pertinent to varied missile jet/plume applications the subject of other review papers. Laboratory jet experiments have served to validate the RANS turbulence models utilized and are supplemented by LES studies to provide data sets not readily obtainable in the laboratory such as temperature fluctuation data needed for thermal transport modeling. Applications for a military fighter aircraft indicate that laboratory experiments cannot replicate the real exhaust environment and thus can only suggest actuation concepts that are promising. CFD is required to revise and scale-up these concepts for the real engine and to provide estimates of their performance in flight. Studies presented show the differences between laboratory plumes and real plumes, as well as the effects of plume/plume and plume/aerodynamic interactions which are quite appreciable and show a markedly different structure than that of the isolated jet under the same operating conditions.

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