Academic literature on the topic 'Logit-normal distribution'

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Journal articles on the topic "Logit-normal distribution"

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Wang, Mingliang, and Keith Rennolls. "Tree diameter distribution modelling: introducing the logit–logistic distribution." Canadian Journal of Forest Research 35, no. 6 (June 1, 2005): 1305–13. http://dx.doi.org/10.1139/x05-057.

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Johnson's SB distribution is a four-parameter distribution that is transformed into a normal distribution by a logit transformation. By replacing the normal distribution of Johnson's SB with the logistic distribution, we obtain a new distributional model that approximates SB. It is analytically tractable, and we name it the "logit–logistic" (LL) distribution. A generalized four-parameter Weibull model and the Burr XII model are also introduced for comparison purposes. Using the distribution "shape plane" (with axes skew2 and kurtosis) we compare the "coverage" properties of the LL, the generalized Weibull, and the Burr XII with Johnson's SB, the beta, and the three-parameter Weibull, the main distributions used in forest modelling. The LL is found to have the largest range of shapes. An empirical case study of the distributional models is conducted on 107 sample plots of Chinese fir. The LL performs best among the four-parameter models.
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Anderson, Simon P., and André de Palma. "Decoupling the CES Distribution Circle with Quality and Beyond: Equilibrium Distributions and the CES-Logit Nexus." Economic Journal 130, no. 628 (February 26, 2020): 911–36. http://dx.doi.org/10.1093/ej/ueaa001.

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Abstract We show for CES demands with heterogeneous productivities that profit, revenue and output distributions lie in the same closed power family as the productivity distribution (e.g., the ‘Pareto circle’). The price distribution lies in the inverse power family. Equilibrium distribution shapes are linked by linear relations between their density elasticities. Introducing product quality decouples the CES circle, and reconciles Pareto price and Pareto sales revenue distributions. We use discrete choice underpinnings to find variable mark-ups for a more flexible demand formulation bridging CES to logit and beyond. For logit demand, exponential (resp. normal) quality-cost distributions generate Pareto (log-normal) economic size distributions.
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Wang, Mingliang, N. I. Ramesh, and Keith Rennolls. "The Richit–Richards family of distributions and its use in forestry." Canadian Journal of Forest Research 37, no. 10 (October 2007): 2052–62. http://dx.doi.org/10.1139/x07-023.

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Johnson’s SB and the logit–logistic are four-parameter distribution models that may be obtained from the standard normal and logistic distributions by a four-parameter transformation. For relatively small data sets, such as diameter at breast height measurements obtained from typical sample plots, distribution models with four or less parameters have been found to be empirically adequate. However, in situations in which the distributions are complex, for example in mixed stands or when the stand has been thinned or when working with aggregated data, then distribution models with more shape parameters may prove to be necessary. By replacing the symmetric standard logistic distribution of the logit–logistic with a one-parameter “standard Richards” distribution and transforming by a five-parameter Richards function, we obtain a new six-parameter distribution model, the “Richit–Richards”. The Richit–Richards includes the “logit–Richards”, the “Richit–logistic”, and the logit–logistic as submodels. Maximum likelihood estimation is used to fit the model, and some problems in the maximum likelihood estimation of bounding parameters are discussed. An empirical case study of the Richit–Richards and its submodels is conducted on pooled diameter at breast height data from 107 sample plots of Chinese fir ( Cunninghamia lanceolata (Lamb.) Hook.). It is found that the new models provide significantly better fits than the four-parameter logit–logistic for large data sets.
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Kim, Seongho, Elisabeth Heath, and Lance Heilbrun. "Sample size determination for logistic regression on a logit-normal distribution." Statistical Methods in Medical Research 26, no. 3 (March 4, 2015): 1237–47. http://dx.doi.org/10.1177/0962280215572407.

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Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.
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Vanbelle, Sophie, and Emmanuel Lesaffre. "Modeling agreement on bounded scales." Statistical Methods in Medical Research 27, no. 11 (May 8, 2017): 3460–77. http://dx.doi.org/10.1177/0962280217705709.

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Agreement is an important concept in medical and behavioral sciences, in particular in clinical decision making where disagreements possibly imply a different patient management. The concordance correlation coefficient is an appropriate measure to quantify agreement between two scorers on a quantitative scale. However, this measure is based on the first two moments, which could poorly summarize the shape of the score distribution on bounded scales. Bounded outcome scores are common in medical and behavioral sciences. Typical examples are scores obtained on visual analog scales and scores derived as the number of positive items on a questionnaire. These kinds of scores often show a non-standard distribution, like a J- or U-shape, questioning the usefulness of the concordance correlation coefficient as agreement measure. The logit-normal distribution has shown to be successful in modeling bounded outcome scores of two types: (1) when the bounded score is a coarsened version of a latent score with a logit-normal distribution on the [0,1] interval and (2) when the bounded score is a proportion with the true probability having a logit-normal distribution. In the present work, a model-based approach, based on a bivariate generalization of the logit-normal distribution, is developed in a Bayesian framework to assess the agreement on bounded scales. This method permits to directly study the impact of predictors on the concordance correlation coefficient and can be simply implemented in standard Bayesian softwares, like JAGS and WinBUGS. The performances of the new method are compared to the classical approach using simulations. Finally, the methodology is used in two different medical domains: cardiology and rheumatology.
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Coull, Brent A., and Alan Agresti. "Random Effects Modeling of Multiple Binomial Responses Using the Multivariate Binomial Logit-Normal Distribution." Biometrics 56, no. 1 (March 2000): 73–80. http://dx.doi.org/10.1111/j.0006-341x.2000.00073.x.

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de Faria, Rute Q., Amanda R. P. dos Santos, Deoclecio J. Amorim, Renato F. Cantão, Edvaldo A. A. da Silva, and Maria M. P. Sartori. "Probit or Logit? Which is the better model to predict the longevity of seeds?" Seed Science Research 30, no. 1 (March 2020): 49–58. http://dx.doi.org/10.1017/s0960258520000136.

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AbstractThe prediction of seed longevity (P50) is traditionally performed by the use of the Probit model. However, due to the fact that the survival data are of binary origin (0,1), the fit of the model can be compromised by the non-normality of the residues. Consequently, this leads to prediction losses, despite the data being partially smoothed by Probit and Logit models. A possibility to reduce the effect of non-normality of the data would be to apply the principles of the central limit theorem, which states that non-normal residues tend to be normal as the n sample is increased. The Logit and Probit models differ in their normal and logistic distribution. Therefore, we developed a new estimation procedure by using a small increase of the n sample and tested it in the Probit and Logit functions to improve the prediction of P50. The results showed that the calculation of P50 by increasing the n samples from 4 to 6 replicates improved the index of correctness of the prediction. The Logit model presented better performance when compared with the Probit model, indicating that the estimation of P50 is more adequate when the adjustment of the data is performed by the Logit function.
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Gorgoso-Varela, Jose Javier, Juan Daniel García-Villabrille, Alberto Rojo-Alboreca, Klaus Von Gadow, and Juan Gabriel Álvarez-González. "Comparing Johnson’s SBB, Weibull and Logit-Logistic bivariate distributions for modeling tree diameters and heights using copulas." Forest Systems 25, no. 1 (April 1, 2016): 07. http://dx.doi.org/10.5424/fs/2016251-08487.

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Aim of study: In this study we compare the accuracy of three bivariate distributions: Johnson’s SBB, Weibull-2P and LL-2P functions for characterizing the joint distribution of tree diameters and heights.Area of study: North-West of Spain.Material and methods: Diameter and height measurements of 128 plots of pure and even-aged Tasmanian blue gum (Eucalyptus globulus Labill.) stands located in the North-west of Spain were considered in the present study. The SBB bivariate distribution was obtained from SB marginal distributions using a Normal Copula based on a four-parameter logistic transformation. The Plackett Copula was used to obtain the bivariate models from the Weibull and Logit-logistic univariate marginal distributions. The negative logarithm of the maximum likelihood function was used to compare the results and the Wilcoxon signed-rank test was used to compare the related samples of these logarithms calculated for each sample plot and each distribution.Main results: The best results were obtained by using the Plackett copula and the best marginal distribution was the Logit-logistic.Research highlights: The copulas used in this study have shown a good performance for modeling the joint distribution of tree diameters and heights. They could be easily extended for modelling multivariate distributions involving other tree variables, such as tree volume or biomass.
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Prastyo, Dedy Dwi, Titis Miranti, and Nur Iriawan. "Survival analysis of companies’ delisting time in Indonesian stock exchange using Bayesian multiple-period logit approach." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4-1 (December 5, 2017): 425–29. http://dx.doi.org/10.11113/mjfas.v13n4-1.864.

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Multiple-period logit model is equivalent to hazard model. This model is able to accommodate time varying predictor. In this work, the parameters of multiple-period model are estimated by using Bayesian inferences. There are three prior distributions used, i.e. improper uniform distribution, multivariate normal distribution, and Cauchy distribution. Criterion which is used to evaluate the proposed technique is C-index. The proposed method is applied to model the delisting time of companies listed in Indonesian Stock Exchange. The survival (delisting) time is driven by firm-specific predictors, i.e. financial ratios, that are calculated from quarterly financial report of companies in manufacturing sector span from the first quarter of 1990 until the third quarter of 2015. Two macroeconomic indicators are also considered as predictors. The empirical results show that the most appropriate prior is multivariate normal distribution. In addition, the proposed model is applied on windowing scheme by reducing the interval time as window in which the model estimator perform by its best.
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Lai, Xinjun, and Jun Li. "Modelling Stochastic Route Choice Behaviours with a Closed-Form Mixed Logit Model." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/729089.

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A closed-form mixed Logit approach is proposed to model the stochastic route choice behaviours. It combines both the advantages of Probit and Logit to provide a flexible form in alternatives correlation and a tractable form in expression; besides, the heterogeneity in alternative variance can also be addressed. Paths are compared by pairs where the superiority of the binary Probit can be fully used. The Probit-based aggregation is also used for a nested Logit structure. Case studies on both numerical and empirical examples demonstrate that the new method is valid and practical. This paper thus provides an operational solution to incorporate the normal distribution in route choice with an analytical expression.
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Dissertations / Theses on the topic "Logit-normal distribution"

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Liu, Jiaping. "A Study on Distribution Learning of Generative Adversarial Networks." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/41250.

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This thesis is an exploration of the properties of shallow generative adversarial networks (GANs). We focus on several aspects of GANs to investigate the learnability of a class of distributions using shallow GANs and conduct experiments to explore the influence of these aspects on the performance of the GAN models. We identify and analyze several pathological phenomena in theoretical analysis and experiments, and propose potential solutions for them.
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Book chapters on the topic "Logit-normal distribution"

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Karakara, Alhassan Abdul-Wakeel, and Evans S. C. Osabuohien. "Categorical Dependent Variables Estimations With Some Empirical Applications." In Applied Econometric Analysis, 164–89. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1093-3.ch008.

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Microeconomic datasets are usually large, mainly survey data. These data are samples of hundreds of respondents or group of respondents (e.g., households). The distributions of such data are mostly not normal because some responses/variables are discrete. Handling such datasets poses some problems of summarizing/reporting the important features of the data in estimations. This study concentrates on how to handle categorical variables in estimation/reporting based on theoretical and empirical knacks. This study used Ghana Demographic and Health Survey data for 2014 for illustration and elaborates on how to interpret results of binary and multinomial outcome regressions. Comparison is made on the different binary models, and binary logit is found to be weighted over the other binary models. Multinomial logistic model is best handled when the odds of one outcome versus the other outcome are independent of other outcome alternatives as verified by the Independent of Irrelevant Alternatives (IIA). Conclusions and suggestions for handling categorical models are discussed in the study.
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Flowerdew, Robin. "Modelling Migration with Poisson Regression." In Technologies for Migration and Commuting Analysis, 261–79. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-61520-755-8.ch014.

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Most statistical analysis is based on the assumption that error is normally distributed, but many data sets are based on discrete data (the number of migrants from one place to another must be a whole number). Recent developments in statistics have often involved generalising methods so that they can be properly applied to non-normal data. For example, Nelder and Wedderburn (1972) developed the theory of generalised linear modelling, where the dependent or response variable can take a variety of different probability distributions linked in one of several possible ways to a linear predictor, based on a combination of independent or explanatory variables. Several common statistical techniques are special cases of the generalised linear models, including the usual form of regression analysis, Ordinary Least Squares regression, and binomial logit modelling. Another important special case is Poisson regression, which has a Poisson-distributed dependent variable, linked logarithmically to a linear combination of independent variables. Poisson regression may be an appropriate method when the dependent variable is constrained to be a non-negative integer, usually a count of the number of events in certain categories. It assumes that each event is independent of the others, though the probability of an event may be linked to available explanatory variables. This chapter illustrates how Poisson regression can be carried out using the Stata package, proceeding to discuss various problems and issues which may arise in the use of the method. The number of migrants from area i to area j must be a non-negative integer and is likely to vary according to zone population, distance and economic variables. The availability of high-quality migration data through the WICID facility permits detailed analysis at levels from the region to the output areas. A vast range of possible explanatory variables can also be derived from the 2001 Census data. Model results are discussed in terms of the significant explanatory variables, the overall goodness of fit and the big residuals. Comparisons are drawn with other analytic techniques such as OLS regression. The relationship to Wilson’s entropy maximising methods is described, and variants on the method are explained. These include negative binomial regression and zero-censored and zero-truncated models.
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Conference papers on the topic "Logit-normal distribution"

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Pierrot, Amandine, and Pierre Pinson. "Adaptive Generalized Logit-Normal Distributions for Wind Power Short-Term Forecasting." In 2021 IEEE Madrid PowerTech. IEEE, 2021. http://dx.doi.org/10.1109/powertech46648.2021.9494900.

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