Least Squares Calibration of the Gravity Model When Intrazonal Flows are Unknown

1983 ◽  
Vol 15 (11) ◽  
pp. 1545-1550 ◽  
Author(s):  
A Sen ◽  
R K Pruthi
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Gravity Model ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Base Period ◽  
Food Grains

Some very fast least-squares based calibration procedures for the gravity model have been presented in earlier papers. Since these procedures are inconvenient or impossible to use when diagonal elements of the base period origin—destination (O—D) matrix are unavailable, one of the procedures has been modified to handle such situations. This modified procedure is described in this paper and then applied to two O—D tables—one for food grains and the other for coal. For these two data sets the procedure yields estimates which are virtually identical to corresponding maximum likelihood estimates.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

Genetic variation and relationships among Afrotropical species of Myotis (Chiroptera: Vespertilionidae)

2019 ◽  
Vol 100 (4) ◽  
pp. 1130-1143 ◽  
Author(s):  
Bruce D Patterson ◽  
Paul W Webala ◽  
Julian C Kerbis Peterhans ◽  
Steven M Goodman ◽  
Michael Bartonjo ◽  
...  
Keyword(s):  
Genetic Variation ◽  
Maximum Likelihood ◽  
Indian Ocean ◽  
Nuclear Data ◽  
The Other ◽  
Data Sets ◽  
Species Trees ◽  
Nuclear Introns ◽  
Geographic Structure ◽  
The Indian Ocean

Abstract The genus Myotis is nearly cosmopolitan and the second-most speciose genus of mammals, but its Afrotropical members are few and poorly known. We analyzed phylogenetic and phylogeographic relationships of six of the eight known Afrotropical species using Cytb and sequences from four nuclear introns. Using Bayesian and maximum-likelihood approaches to generate single-locus, concatenated, and species trees, we confirmed prior evidence that the clade containing Afrotropical Myotis also contains both Palearctic and Indomalayan members. Additionally, we demonstrate that M. bocagii is sister to the Indian Ocean species M. anjouanensis, that this group is sister to M. tricolor and the Palearctic M. emarginatus, and find evidence suggesting that M. welwitschii is the earliest-diverging Afrotropical species and sister to the remainder. Although M. tricolor and M. welwitschii are both currently regarded as monotypic, both mitochondrial and nuclear data sets document significant, largely concordant geographic structure in each. Evidence for the distinction of two lineages within M. tricolor is particularly strong. On the other hand, geographic structure is lacking in M. bocagii, despite the current recognition of two subspecies in that species. Additional geographic sampling (especially at or near type localities), finer-scale sampling (especially in zones of sympatry), and integrative taxonomic assessments will be needed to better document this radiation and refine its nomenclature.

scholarly journals Simple penalties on maximum likelihood estimates of genetic parameters to reduce sampling variation

2015 ◽  
Author(s):  
karin meyer
Keyword(s):  
Maximum Likelihood ◽  
Genetic Parameters ◽  
Likelihood Function ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Simple Modification ◽  
Scale Free ◽  
Wide Range ◽  
Sampling Variation ◽  
The Difference

Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by substantially reducing their sampling variances. This is achieved maximizing the likelihood subject to a penalty. Borrowing from Bayesian principles, we propose a mild, default penalty -- derived assuming a Beta distribution of scale-free functions of the covariance components to be estimated -- rather than laboriously attempting to determine the stringency of penalization from the data. An extensive simulation study is presented demonstrating that such penalties can yield very worthwhile reductions in loss, i.e. the difference from population values, for a wide range of scenarios and without distorting estimates of phenotypic covariances. Moreover, mild default penalties tend not to increase loss in difficult cases and, on average, achieve reductions in loss of similar magnitude than computationally demanding schemes to optimize the degree of penalization. Pertinent details required for the adaptation of standard algorithms to locate the maximum of the likelihood function are outlined.

scholarly journals Voxel-wise and spatial modelling of binary lesion masks: A review and comparison of methods

2021 ◽  
Author(s):  
Petya Kindalova ◽  
Ioannis Kosmidis ◽  
Thomas E. Nichols
Keyword(s):  
Maximum Likelihood ◽  
Spatial Dependence ◽  
Reference Data ◽  
Spatial Modelling ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Computationally Efficient ◽  
Data Set ◽  
Lesion Mapping ◽  
Modelling Approach

AbstractObjectivesWhite matter lesions are a very common finding on MRI in older adults and their presence increases the risk of stroke and dementia. Accurate and computationally efficient modelling methods are necessary to map the association of lesion incidence with risk factors, such as hypertension. However, there is no consensus in the brain mapping literature whether a voxel-wise modelling approach is better for binary lesion data than a more computationally intensive spatial modelling approach that accounts for voxel dependence.MethodsWe review three regression approaches for modelling binary lesion masks including massunivariate probit regression modelling with either maximum likelihood estimates, or mean bias-reduced estimates, and spatial Bayesian modelling, where the regression coefficients have a conditional autoregressive model prior to account for local spatial dependence. We design a novel simulation framework of artificial lesion maps to compare the three alternative lesion mapping methods. The age effect on lesion probability estimated from a reference data set (13,680 individuals from the UK Biobank) is used to simulate a realistic voxel-wise distribution of lesions across age. To mimic the real features of lesion masks, we suggest matching brain lesion summaries (total lesion volume, average lesion size and lesion count) across the reference data set and the simulated data sets. Thus, we allow for a fair comparison between the modelling approaches, under a realistic simulation setting.ResultsOur findings suggest that bias-reduced estimates for voxel-wise binary-response generalized linear models (GLMs) overcome the drawbacks of infinite and biased maximum likelihood estimates and scale well for large data sets because voxel-wise estimation can be performed in parallel across voxels. Contrary to the assumption of spatial dependence being key in lesion mapping, our results show that voxel-wise bias-reduction and spatial modelling result in largely similar estimates.ConclusionBias-reduced estimates for voxel-wise GLMs are not only accurate but also computationally efficient, which will become increasingly important as more biobank-scale neuroimaging data sets become available.

scholarly journals On Use of the Standard Deviation of the Mass Distribution as a Parameter in Raindrop Size Distribution Functions

2019 ◽  
Vol 58 (4) ◽  
pp. 787-796 ◽  
Author(s):  
Paul L. Smith ◽  
Roger W. Johnson ◽  
Donna V. Kliche
Keyword(s):  
Standard Deviation ◽  
Maximum Likelihood ◽  
Size Distribution ◽  
Mass Distribution ◽  
Shape Parameter ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Moment Methods ◽  
Raindrop Size Distribution ◽  
Raindrop Size

AbstractUse of the standard deviation σm of the drop mass distribution as one of the three parameters of raindrop size distribution (DSD) functions was introduced for application to disdrometer data supporting the Global Precipitation Measurement dual-frequency radar system. The other two parameters are a normalized drop number concentration Nw and the mass-weighted mean diameter Dm. This paper presents an evaluation of that formulation of the DSD functions, in two parts. First is a mathematical analysis showing that the procedure for estimating σm, along with the other DSD parameters, from disdrometer data is in essence another moment method. As such, it is subject to the biases and errors inherent in all moment methods. When the form of the DSD function is specified, it is inferior (like all moment methods) to the maximum likelihood technique for fitting parameters to sampled data. The second part is a series of sampling simulations illustrating the biases and errors involved in applying the formulation to the specific case of gamma DSDs. It leads to underestimates of σm and consequently to overestimates of the gamma shape parameter—with large root-mean-square errors. Comparison with maximum likelihood estimates shows the degree of improvement that could be obtained in the estimates of the shape parameter. The propensity to underestimate σm will be pervasive, and users of this DSD formulation should be cognizant of the biases and errors that can occur.

scholarly journals A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 32-47
Author(s):  
Gauss Cordeiro ◽  
Maria de Lima ◽  
Edwin Ortega ◽  
Adriano Suzuki
Keyword(s):  
Maximum Likelihood ◽  
Regression Model ◽  
Real Data ◽  
Random Variable ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Poisson Random Variable ◽  
Fatigue Lifetime ◽  
Special Cases ◽  
New Distribution

We propose an extended fatigue lifetime model called the odd log-logistic Birnbaum–Saunders–Poisson distribution, which includes as special cases the Birnbaum–Saunders and odd log-logistic Birnbaum–Saunders distributions. We obtain some structural properties of the new distribution. We define a new extended regression model based on the logarithm of the odd log-logistic Birnbaum–Saunders–Poisson random variable. For censored data, we estimate the parameters of the regression model using maximum likelihood. We investigate the accuracy of the maximum likelihood estimates using Monte Carlo simulations. The importance of the proposed models, when compared to existing models, is illustrated by means of two real data sets.

Modeling the Stability of Fish Schools: Exchange of Individual Fish between Schools of Skipjack Tuna (Katsuwonus pelamis)

1991 ◽  
Vol 48 (6) ◽  
pp. 1081-1091 ◽  
Author(s):  
Ray Hilborn
Keyword(s):  
Maximum Likelihood ◽  
Exchange Model ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Skipjack Tuna ◽  
Katsuwonus Pelamis ◽  
Fish Schools ◽  
Individual Fish ◽  
The Stability

Three data sets that involve intensive mark and recapture of schools of skipjack tuna (Katsuwonus pelamis) are examined for information about exchange of individuals between schools. A formal exchange model is proposed, and maximum likelihood estimates of the parameters are found. It appears that individuals exchange quite rapidly between schools of skipjack; 16–63% of individuals apparently leave a school each day to join other schools. It is possible, however, that what are operationally defined as schools by fishermen consist of smaller more stable subunits.

scholarly journals Mixtures and products in two graphical models

2018 ◽  
Vol 9 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Anna Seigal ◽  
Guido Montufar
Keyword(s):  
Maximum Likelihood ◽  
Closed Form ◽  
Graphical Models ◽  
Statistical Models ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Boltzmann Machine ◽  
Algebraic Description ◽  
Binary Random Variables ◽  
Probability Simplex

We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their parametrizations, we show that they represent the same set of distributions on the interior of the probability simplex, and are equal up to closure. We give a semi-algebraic description of the model in terms of six binomial inequalities and obtain closed form expressions for the maximum likelihood estimates. We briefly discuss extensions to larger models.

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