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Relevant bibliographies by topics / Negative binomial distribution. Parameter estimation

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Academic literature on the topic 'Negative binomial distribution. Parameter estimation'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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Journal articles on the topic "Negative binomial distribution. Parameter estimation"

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Famoye, Felix. "Parameter estimation for generalized negative binomial distribution." Communications in Statistics - Simulation and Computation 26, no. 1 (1997): 269–79. http://dx.doi.org/10.1080/03610919708813378.

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Whitaker, Thomas, Francis Giesbrecht, and Jeremy Wu. "Suitability of Several Statistical Models to Simulate Observed Distribution of Sample Test Results in Inspections of Aflatoxin-Contaminated Peanut Lots." Journal of AOAC INTERNATIONAL 79, no. 4 (1996): 981–88. http://dx.doi.org/10.1093/jaoac/79.4.981.

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Abstract The acceptability of 10 theoretical distributions to simulate observed distribution of sample aflatoxin test results was evaluated by using 2 parameter estimation methods and 3 goodness of fit (GOF) tests. All theoretical distributions were compared with 120 observed distributions of aflatoxin test results of farmers' stock peanuts. For a given parameter estimation method and GOF test, the negative binomial distribution had the highest percentage of statistically acceptable fits. The log normal and Poisson-gamma (gamma shape parameter = 0.5) distributions had slightly fewer but an almost equal percentage of acceptable fits. For the 3 most acceptable statistical models, the negative binomial had the greatest percentage of best or closest fits. Both the parameter estimation method and the GOF test had an influence on which theoretical distribution had the largest number of acceptable fits. All theoretical distributions, except the negative binomial distribution, had more acceptable fits when model parameters were determined by the maximum likelihood method. The negative binomial had slightly more acceptable fits when model parameters were estimated by the method of moments. The results also demonstrated the importance of using the same GOF test for comparing the acceptability of several theoretical distributions.

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Wang, Yining. "Estimation problems for the two-parameter negative binomial distribution." Statistics & Probability Letters 26, no. 2 (1996): 113–14. http://dx.doi.org/10.1016/0167-7152(94)00259-2.

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Aryuyuen, Sirinapa, and Issaraporn Thiamsorn. "Methods for Parameter Estimation of the Negative Binomial-Generalized Exponential Distribution." Applied Mechanics and Materials 866 (June 2017): 383–86. http://dx.doi.org/10.4028/www.scientific.net/amm.866.383.

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Abstract. We proposed several estimation methods for the parameters of the negative binomial-generalized exponential (NB-GE) distribution. In the simulation study, the maximum likelihood estimation (MLE) with nlm function seems to have the most efficiency to estimate the parameters and of the NB-GE distribution when it compares with method of the moments (MM) and MLE with optim function by using the average mean square error (AMSE) for a criteria. The AMSE values of each parameter estimation methods are decreasing when the sample size increasing. Moreover, the example dataset is illustrated. Based on the chi-square values for the fitting distribution via the MLE with nlm function is better than other estimation methods.

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Al-Saleh, Mohammad F., and Fatima K. Al-Batainah. "Estimation of the shape parameter k of the negative binomial distribution." Applied Mathematics and Computation 143, no. 2-3 (2003): 431–41. http://dx.doi.org/10.1016/s0096-3003(02)00374-0.

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Shanker, Rama, and Kamlesh Kumar Shukla. "A new three-parameter size-biased poisson-lindley distribution with properties and applications." Biometrics & Biostatistics International Journal 9, no. 1 (2020): 1–4. http://dx.doi.org/10.15406/bbij.2020.09.00294.

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A new three-parameter size-biased Poisson-Lindley distribution which includes several one parameter and two-parameter size-biased distributions including size-biased geometric distribution (SBGD), size-biased negative binomial distribution (SBNBD), size-biased Poisson-Lindley distribution (SBPLD), size-biased Poisson-Shanker distribution (SBPSD), size-biased two-parameter Poisson-Lindley distribution-1 (SBTPPLD-1), size-biased two-parameter Poisson-Lindley distribution-2(SBTPPLD-2), size-biased quasi Poisson-Lindley distribution (SBQPLD) and size-biased new quasi Poisson-Lindley distribution (SBNQPLD) for particular cases of parameters has been proposed. Its various statistical properties based on moments including coefficient of variation, skewness, kurtosis and index of dispersion have been studied. Maximum likelihood estimation has been discussed for estimating the parameters of the distribution. Goodness of fit of the proposed distribution has been discussed.

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Lee, Simon CK. "Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing." Risks 8, no. 1 (2020): 19. http://dx.doi.org/10.3390/risks8010019.

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This study proposes an efficacious approach to analyze the over-dispersed insurance frequency data as it is imperative for the insurers to have decisive informative insights for precisely underwriting and pricing insurance products, retaining existing customer base and gaining an edge in the highly competitive retail insurance market. The delta boosting implementation of the negative binomial regression, both by one-parameter estimation and a novel two-parameter estimation, was tested on the empirical data. Accurate parameter estimation of the negative binomial regression is complicated with considerations of incomplete insurance exposures, negative convexity, and co-linearity. The issues mainly originate from the unique nature of insurance operations and the adoption of distribution outside the exponential family. We studied how the issues could significantly impact the quality of estimation. In addition to a novel approach to simultaneously estimate two parameters in regression through boosting, we further enrich the study by proposing an alteration of the base algorithm to address the problems. The algorithm was able to withstand the competition against popular regression methodologies in a real-life dataset. Common diagnostics were applied to compare the performance of the relevant candidates, leading to our conclusion to move from light-tail Poisson to negative binomial for over-dispersed data, from generalized linear model (GLM) to boosting for non-linear and interaction patterns, from one-parameter to two-parameter estimation to reflect more closely the reality.

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Elsaied, Hanan, and Roland Fried. "On robust estimation of negative binomial INARCH models." METRON 79, no. 2 (2021): 137–58. http://dx.doi.org/10.1007/s40300-021-00207-8.

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AbstractWe discuss robust estimation of INARCH models for count time series, where each observation conditionally on its past follows a negative binomial distribution with a constant scale parameter, and the conditional mean depends linearly on previous observations. We develop several robust estimators, some of them being computationally fast modifications of methods of moments, and some rather efficient modifications of conditional maximum likelihood. These estimators are compared to related recent proposals using simulations. The usefulness of the proposed methods is illustrated by a real data example.

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Van De Ven, R. "Estimating the shape parameter for the negative binomial distribution." Journal of Statistical Computation and Simulation 46, no. 1-2 (1993): 111–23. http://dx.doi.org/10.1080/00949659308811497.

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Savani, V., and A. A. Zhigljavsky. "Efficient Estimation of Parameters of the Negative Binomial Distribution." Communications in Statistics - Theory and Methods 35, no. 5 (2006): 767–83. http://dx.doi.org/10.1080/03610920500501346.

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Dissertations / Theses on the topic "Negative binomial distribution. Parameter estimation"

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Chang, Yu-Chen, and 張妤真. "A simulation study on estimation of the clumping parameter of a negative binomial distribution." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/40123732756803862450.

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Δίκαρος, Ανδρέας. "Αρνητική διωνυμική κατανομή και εκτίμηση των παραμέτρων της". Thesis, 2010. http://nemertes.lis.upatras.gr/jspui/handle/10889/3990.

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Η παρούσα μεταπτυχιακή διατριβή εντάσσεται ερευνητικά στην περιοχή της Στατιστικής θεωρίας Αποφάσεων και ειδικότερα στη μελέτη της αρνητικής διωνυμικής κατανομής καθώς επίσης και στην εκτίμηση των παραμέτρων της. Στο Κεφάλαιο 1 παρουσιάζονται κάποιοι χρήσιμοι, για την πορεία της μελέτης μας, ορισμοί και θεωρήματα. Στο Κεφάλαιο 2 μελετάται το μοντέλο της αρνητικής διωνυμικής κατανομής, δίνονται τα χαρακτηριστικά μεγέθη αυτής και παρουσιάζονται οι διαφορετικές παραμετρικοποιήσεις της. Στο Κεφάλαιο 3, εξετάζεται το πρόβλημα εκτίμησης των παραμέτρων της αρνητικής διωνυμικής κατανομής και πιο ειδικά η εκτίμηση για τις διάφορες παραμετρικοποιήσης της. Για περισσότερη ανάλυση χρησιμοποιούνται η εκτίμηση μέγιστης πιθανοφάνειας, η εκτίμηση με τη μέθοδο των ροπών και πιο εξειδικευμένες υπολογιστικές μέθοδοι εκτίμησης. Στο Κεφάλαιο 4, και για το ίδιο πρόβλημα εκτίμησης που πραγματεύεται το προηγούμενο κεφάλαιο, επιλέγεται ο βέλτιστος εκτιμητής των παραμέτρων της αρνητικής διωνυμικής κατανομής και παρουσιάζεται ένα παράδειγμα για την κατανόηση των μεθόδων εκτίμησης.<br>The master thesis we are going to introduce takes place in the region of Statistical Decision Theory and particularly in studying the Negative Binomial Distribution and the estimation of its parameters. In Chapter 1 some useful definitions and theorems are presented. In Chapter 2 the model of negative binomial distribution is studied and its different parameterizations are discussed. In Chapter 3 we examine the problem of estimating the parameters of our model and for its parameterizations. In particular we give the method of Maximum Likelihood Estimation, the Method of Moments and more specified Estimation Methods. In Chapter 4 and for the same estimation problem, as in previous chapter, it’s been chosen the best estimator of the parameters in our model and it’s been derived an example for the better understanding of the above methods.

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Tuyl, Frank Adrianus Wilhelmus Maria. "Estimation of the Binomial parameter: in defence of Bayes (1763)." 2007. http://hdl.handle.net/1959.13/25730.

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Research Doctorate - Doctor of Philosophy (PhD)<br>Interval estimation of the Binomial parameter è, representing the true probability of a success, is a problem of long standing in statistical inference. The landmark work is by Bayes (1763) who applied the uniform prior to derive the Beta posterior that is the normalised Binomial likelihood function. It is not well known that Bayes favoured this ‘noninformative’ prior as a result of considering the observable random variable x as opposed to the unknown parameter è, which is an important difference. In this thesis we develop additional arguments in favour of the uniform prior for estimation of è. We start by describing the frequentist and Bayesian approaches to interval estimation. It is well known that for common continuous models, while different in interpretation, frequentist and Bayesian intervals are often identical, which is directly related to the existence of a pivotal quantity. The Binomial model, and its Poisson sister also, lack a pivotal quantity, despite having sufficient statistics. Lack of a pivotal quantity is the reason why there is no consensus on one particular estimation method, more so than its discreteness: frequentist (unconditional) coverage depends on è. Exact methods guarantee minimum coverage to be at least equal to nominal and approximate methods aim for mean coverage to be close to nominal. We agree with what seems like the majority of frequentists, that exact methods are too conservative in practice, and show additional undesirable properties. This includes more recent ‘short’ exact intervals. We argue that Bayesian intervals based on noninformative priors are preferable to the family of frequentist approximate intervals, some of which are wider than exact intervals for particular data values. A particular property of the interval based on the uniform prior is that its mean coverage is exactly equal to nominal. However, once committed to the Bayesian approach there is no denying that the current preferred choice, by ‘objective’ Bayesians, is the U-shaped Jeffreys prior which results from various methods aimed at finding noninformative priors. The most successful such method seems to be reference analysis which has led to sensible priors in previously unsolved problems, concerning multiparameter models that include ‘nuisance’ parameters. However, we argue that there is a class of models for which the Jeffreys/reference prior may be suboptimal and that in the case of the Binomial distribution the requirement of a uniform prior predictive distribution leads to a more reasonable ‘consensus’ prior.

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El-Khatib, Mayar. "Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement." Thesis, 2010. http://hdl.handle.net/10012/5741.

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While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond.

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Book chapters on the topic "Negative binomial distribution. Parameter estimation"

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Gorshenin, Andrey, and Victor Korolev. "A Functional Approach to Estimation of the Parameters of Generalized Negative Binomial and Gamma Distributions." In Developments in Language Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99447-5_30.

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Ogutu, Carolyne, and Antony Rono. "On Modelling Extreme Damages from Natural Disasters in Kenya." In Natural Hazards - Impacts, Adjustments and Resilience. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.94578.

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We seek to develop a distribution to model the extreme damages resulting from Natural Disasters in Kenya.The distribution is based on the Compound Extreme Value Distribution, which takes into account both the distributions of the frequency of occurrence and magnitude of the events. Threshold modelling is employed, where the extreme damages are identified as the points that lie above a sufficiently high threshold. The distribution of the number of the exceedance is found to be Negative Binomial, while that of the severity is approximated by a Generalised Pareto Distribution. Maximum likelihood estimation is used to estimate the parameters, and the log-likelihood is maximised using numerical methods. Probability weighted moments estimation is used to determine the starting values for the iterations. Prediction study is then carried out to investigate the performance of the proposed distribution in predicting future events.

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"ON ESTIMATION AND GROUP CLASSIFICATION IN THE SPACE OF A SUFFICIENT STATISTIC OF THE NEGATIVE BINOMIAL DISTRIBUTION." In Probabilistic Methods in Discrete Mathematics. De Gruyter, 2002. http://dx.doi.org/10.1515/9783112314104-012.

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Veech, Joseph A. "Statistical Methods for Analyzing Species–Habitat Associations." In Habitat Ecology and Analysis. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198829287.003.0009.

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Six methods for statistically identifying and quantifying meaningful species–habitat associations are discussed. These are (1) comparison among group means (e.g. ANOVA), (2) multiple linear regression, (3) multiple logistic regression, (4) classification and regression trees, (5) multivariate techniques (principal components analysis and discriminant function analysis), and (6) occupancy modeling. Each method is described in statistical detail and associated terminology is explained. The example of habitat associations of a hypothetical beetle species (from Chapter 8) is used to further explain some of the methods. Assumption, strengths, and weaknesses of each method are discussed. Related statistical constructs and procedures such as the variance–covariance matrix, negative binomial distribution, generalized linear modeling, maximum likelihood estimation, and Bayes’ theorem are also explained. Some historical context is provided for some of the methods.

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Conference papers on the topic "Negative binomial distribution. Parameter estimation"

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Sirichantra, Chutima, and Winai Bodhisuwan. "Parameter estimation of the zero inflated negative binomial beta exponential distribution." In PROCEEDINGS OF THE 13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5012260.

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Prasongporn, Pralongpol, and Winai Bodhisuwan. "Negative Binomial - Two Parameter Weighted Exponential (NB-TWE) Distribution." In 5th Annual International Conference on Operations Research and Statistics (ORS 2017). Global Science & Technology Forum (GSTF), 2017. http://dx.doi.org/10.5176/2251-1938_ors17.18.

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Denthet, Sunthree, Ampai Thongteeraparp, and Winai Bodhisuwan. "Mixed distribution of negative binomial and two-parameter Lindley distributions." In 2016 12th International Conference on Mathematics, Statistics, and Their Application (ICMSA). IEEE, 2016. http://dx.doi.org/10.1109/icmsa.2016.7954318.

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Sun, Zengguo, and Chongzhao Han. "Parameter Estimation of Positive Alpha-Stable Distribution Based on Negative-Order Moments." In 2007 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, 2007. http://dx.doi.org/10.1109/icassp.2007.367110.

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Watson, Bryan C., and Cassandra Telenko. "Binomial Parameter Determination and Mapping for Demand Prediction: A Case Study of Bike Sharing Station Expansion Design." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87865.

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Quantitative approaches to estimating user demand provide a powerful tool for engineering designers. We hypothesized that estimating binomial distribution parameters n (user population size) and p (user population product affinity) from historical user data can predict demand in new situations. This approach applied to a major Bike Sharing System (BSS) expansion. BSS Operators must make key decisions when adding additional docking stations. Binomial Parameter estimation approaches are briefly discussed, followed by evidence that BSSs supply an amiable case for parameter estimation. Parameter plots reveal a continuous surface over the BSS area. These surfaces allow prediction of overall ridership levels at new station locations distinctly and more accurately from approaches currently utilized. Utilizing spearman’s Rho as a comparison benchmark, our approach yields a stronger correlation between our prediction and the observed new station utilization (rho = .830, stations = 46, p < .01) than the order implemented by the BSS operator (rho = .596, stations = 46, p < .01). Finally, this approach is mathematically straightforward, indicating potential as a mainstream BSS tool for BSS operators planning future station expansions. The results validate our approach of using current user data to determine target population characteristics, informing decisions about new design situations.

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Khalil, Mohammad, Abhijit Sarkar, and Dominique Poirel. "Parameter Estimation of a Fluttering Aeroelastic System in the Transitional Reynolds Number Regime." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30047.

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We report the parameter estimation results of a self-sustaining aeroelastic oscillator. The system is composed of a rigid wing that is elastically mounted on a rig, which in turn is fixed in a wind tunnel. For certain flow conditions, in particular dictated by the Reynolds number in the transitional regime, the wing extracts energy from the flow leading to a stable limit cycle oscillation. The basic physical mechanism at the origin of the oscillations is laminar boundary layer separation, which leads to negative aerodynamic damping. An empirical model of the aeroelastic system is proposed in the form of a generalized Duffing-van der Pol oscillator, whereby the linear and nonlinear aeroelastic terms are unknowns to be estimated. The model (input) noise process accounting for the amplitude modulation observed from experiments will also be estimated. We apply a Bayesian inference based batch data assimilation method in tackling this strongly nonlinear and non-Gaussian model. In particular, Markov Chain Monte Carlo sampling technique is used to generate samples from the joint distribution of the unknown parameters given noisy measurement data. The extended Kalman filter is utilized to obtain the conditional distribution of the model state given the noisy measurements. The parameter estimates for a third order generalized Duffing-van der Pol oscillator are obtained and marginal and joint probability density functions for the parameters will be presented for both a numerical model and a rigid wing that is elastically mounted on a rig in a wind tunnel.

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