scholarly journals Fit Adequacy of Dichotomous Logit Response Models of the Regressor Bernoulli and Binomial Probability Distributions

2016 ◽  
Vol 16 ◽  
pp. 38-48
Author(s):  
G. Uzodinma Ugwuanyim ◽  
Chukwudi Justin Ogbonna
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Models ◽  
Response Models ◽  
Explanatory Variables ◽  
Fit Statistics ◽  
Binomial Distributions ◽  
Multiple Correlation Analysis ◽  
Work Done ◽  
Best Fit

Logit models belong to the class of probability models that determine discrete probabilities over a limited number of possible outcomes. They are often called ‘Quantal Variables’ or ‘Stimulus and Response Models’ in Biological Literature. The conventional R2 measure of goodness-of-fit is problematic in logit models. This has therefore led to the proposal of several alternative goodness-of-fit measures. But researchers in this area have identified the base rate problem in using these several alternative goodness-of-fit measures. This research is an extension of work done by people in this area. Specifically, this research is aimed at investigating the goodness-of-fit performances of eight statistics using the Bernoulli and Binomial distributions as explanatory variables under various scenarios. The study will draw conclusions on the “best” fit. The data for the study was generated through simulation and analysed using the multiple correlation analysis. The findings clearly show that for the Bernoulli Distribution, the goodness-of-fit statistics to use are: RO2, RC2, RM2 and λp; and for the Binomial Distribution, the goodness-of-fit statistics to use are: and RN2 and λp. RO2 stood out as the “best” goodness-of-fit statistics.

scholarly journals A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

2016 ◽  
Vol 11 (1) ◽  
pp. 432-440 ◽  
Author(s):  
M. T. Amin ◽  
M. Rizwan ◽  
A. A. Alazba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Future Research ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Northern Regions ◽  
Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

scholarly journals Allometric Equations for Volume, Biomass, and Carbon in Commercial Stems Harvested in a Managed Forest in the Southwestern Amazon: A Case Study

Forests ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 874 ◽  
Author(s):  
Flora Magdaline Benitez Romero ◽  
Laércio Antônio Gonçalves Jacovine ◽  
Sabina Cerruto Ribeiro ◽  
Carlos Moreira Miquelino Eleto Torres ◽  
Liniker Fernandes da Silva ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Nonlinear Models ◽  
Allometric Equations ◽  
Managed Forest ◽  
Absolute Deviation ◽  
Explanatory Variables ◽  
Commercial Species ◽  
Linear And Nonlinear ◽  
Ecological Importance ◽  
Best Fit

Forests in the southwestern Amazon are rich, diverse, and dense. The region is of high ecological importance, is crucial for conservation and management of natural resources, and contains substantial carbon and biodiversity stocks. Nevertheless, few studies have developed allometric equations for this part of the Amazon, which differs ecologically from the parts of Amazonia where most allometric studies have been done. To fill this gap, we developed allometric equations to estimate the volume, biomass, and carbon in commercial trees with diameter at breast height (DBH) ≥ 50 cm in an area under forest management in the southeastern portion of Brazil’s state of Acre. We applied the Smalian formula to data collected from 223 felled trees in 20 species, and compared multiple linear and nonlinear models. The models used diameter (DBH) measured at 1.30 m height (d), length of the commercial stem (l), basic wood density (p), and carbon content (t), as independent variables. For each dependent variable (volume, biomass, or carbon) we compared models using multiple measures of goodness-of-fit, as well as graphically analyzing residuals. The best fit for estimating aboveground volume of individual stems using diameter (d) and length (l) as variables was obtained with the Spurr model (1952; logarithmic) (root mean square error (RMSE) = 1.637, R² = 0.833, mean absolute deviation (MAD) = 1.059). The best-fit equation for biomass, considering d, l, and p as the explanatory variables, was the Loetsch et al. (1973; logarithmic) model (RMSE = 1.047, R² = 0.855, MAD = 0.609). The best fit equation for carbon was the Loetsch et al. (1973; modified) model, using the explanatory variables d, l, p, and t (RMSE = 0.530, R² = 0.85, MAD = 0.304). Existing allometric equations applied to our study trees performed poorly. We showed that the use of linear and nonlinear allometric equations for volume, biomass, and carbon can reduce the errors and improve the estimation of these metrics for the harvested stems of commercial species in the southwestern Amazon.

Binary response models comparison using the 𝛼-Chernoff divergence measure and exponential integral functions

2021 ◽  
pp. 37-53
Author(s):  
Subir Ghosh ◽  
Hans Nyquist
Keyword(s):  
Probability Distributions ◽  
Binary Response ◽  
Divergence Measure ◽  
Exponential Integral ◽  
Response Models ◽  
Content Type ◽  
Explanatory Variables ◽  
Criterion Functions ◽  
Models Comparison ◽  
Binary Response Models

In this paper, the families of binary response models are describing the data on a response variable having two possible outcomes and p p explanatory variables when the possible responses and their probabilities are functions of the explanatory variables. The α \alpha -Chernoff divergence measure and the Bhattacharyya divergence measure when α = 1 / 2 \alpha = 1/2 are the criterion functions used for quantifying the dissimilarity between probability distributions by expressing the divergence measures in terms of the exponential integral functions. The dependences of odds ratio and hazard function on the explanatory variables are also a part of the modeling.

Estimate the probability density function of maximum temperature for the Middle East

2020 ◽  
Vol 29 (4) ◽  
pp. 517-531
Author(s):  
Iqbal Al-Ataby ◽  
Amani Al-Tmimi
Keyword(s):  
Middle East ◽  
Goodness Of Fit ◽  
Heat Waves ◽  
Probability Distributions ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Logistic Distribution ◽  
Recent Past ◽  
Ecmwf Model ◽  
Best Fit

Pollution is one reasons for increase temperature which leads to increase the heat waves which have large socioeconomic and healthy impacts on Middle East. By using monthly daily mean of maximum temperature (C°) at height (2m) covered middle east as a grid of (1581) points for selected months (March, April, May) represent spring and (Jun, July, August) represent Summer for the period 1979 to2018, from the ECMWF, model ERA-interim. Many PDFs have been proposed in recent past, but in present study Logistic, Rayleigh and Gamma distribution are used to describe the characteristics of maximum temperature. This paper attempts to determine the best fitted probability distribution of maximum temperature. To check the accuracy of the predicted data using theoretical probability distributions the goodness of fit criteria Z-test used in this paper. According to the goodness-of-fit criteria and from the graphical comparisons it can be said that Logistic distribution provides the best fit for the observed monthly daily mean of maximum temperature data.

scholarly journals Estimate of intense rainfall equation parameters for rainfall stations of the Paraíba State, Brazil

2017 ◽  
Vol 47 (1) ◽  
pp. 15-21
Author(s):  
Alcinei Ribeiro Campos ◽  
João Batista Lopes da Silva ◽  
Glenio Guimarães Santos ◽  
Rafael Felippe Ratke ◽  
Itauane Oliveira de Aquino
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Daily Rainfall ◽  
Water Source ◽  
Rainfall Data ◽  
Intense Rainfall ◽  
Probability Models ◽  
Temporal And Spatial Distribution ◽  
Intensity Duration Frequency ◽  
Log Normal

ABSTRACT Rainfall is the primary water source for hydrographic basins. Hence, the quantification and knowledge of its temporal and spatial distribution are indispensable in dimensioning hydraulic projects. This study aimed at assessing the fit of a series of rainfall data to different probability models, as well as estimating parameters of the intensity-duration-frequency (IDF) equation for rain stations of the Paraíba State, Brazil. The rainfall data of each station were obtained from the Brazilian Water Agency databanks. To estimate the maximum daily rainfall of each station and return period (5, 10, 15, 25, 50 and 100 years), the following probability distributions were used: Gumbel, Log-Normal II, Log-Normal III, Pearson III and Log-Pearson III. The estimation of rainfall in durations of 5-1,440 min was carried out by daily rainfall disaggregation. The adjustment of the IDF equation was performed via nonlinear multiple regression, using the nonlinear generalized reduced gradient interaction method. When compared to the data observed, the intense rainfall equations for most stations showed goodness of fit with coefficients of determination above 0.99, which supports the methodology applied in this study.

scholarly journals Establishment of a Stochastic Model for Sustainable Economic Flood Management in Yewa Sub-Basin, Southwest Nigeria

2016 ◽  
Vol 2 (12) ◽  
pp. 646-655 ◽  
Author(s):  
O.A Agbede ◽  
Oluwatobi Aiyelokun
Keyword(s):  
Probability Distribution ◽  
Stochastic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Flood Management ◽  
Return Periods ◽  
Probability Models ◽  
Goodness Of Fit Test ◽  
Southwest Nigeria ◽  
Anderson Darling

Of all natural disasters, floods have been considered to have the greatest potential damage. The magnitude of economic damages and number of people affected by flooding have recently increased globally due to climate change. This study was based on the establishment of a stochastic model for reducing economic floods risk in Yewa sub-basin, by fitting maximum annual instantaneous discharge into four probability distributions. Daily discharge of River Yewa gauged at Ijaka-Oke was used to establish a rating curve for the sub-basin, while return periods of instantaneous peak floods were computed using the Hazen plotting position. Flood magnitudes were found to increase with return periods based on Hazen plotting position. In order to ascertain the most suitable probability distribution for predicting design floods, the performance evaluation of the models using root mean square error was employed. In addition, the four probability models were subjected to goodness of fit test besed on Anderson-Darling (A2) and Kolmogorov-Smirnov (KS). As a result of the diagnostics test the Weibul probability distribution was confirmed to fit well with the empirical data of the study area. The stochastic model  generated from the Weibul probability distribution, could be used to enhance sustainable development by reducing economic flood damages in the sub-basin.

scholarly journals Distribution of Earthquake Magnitude Levels in Bangladesh

2019 ◽  
Vol 11 (3) ◽  
pp. 15
Author(s):  
Md. Habibur Rahman ◽  
Md. Moyazzem Hossain
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Earthquake Magnitude ◽  
Human Beings ◽  
Richter Scale ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Best Fit

Earthquakes are one of the main natural hazards which seriously make threats the life and property of human beings. Different probability distributions of the earthquake magnitude levels in Bangladesh are fitted. In terms of graphical assessment and goodness-of-fit criterion, the log-normal distribution is found to be the best fit probability distributions for the earthquake magnitude levels in Bangladesh among the probability distribution considered in this study. The average earthquake magnitude level found 4.67 (in Richter scale) for log-normal distribution and the approximately forty-six percent chance is predicted to take place earthquake magnitude in the interval four to five.

scholarly journals Representing Accessibility: Evidence from Vehicle Ownership Choices and Property Valuations in Singapore

2019 ◽  
Vol 2673 (2) ◽  
pp. 724-733 ◽  
Author(s):  
He He ◽  
Roberto Ponce-Lopez ◽  
Jingsi Shaw ◽  
Diem-Trinh Le ◽  
Joseph Ferreira ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Explanatory Power ◽  
Market Price ◽  
Real Estate Market ◽  
Vehicle Ownership ◽  
Explanatory Variables ◽  
Fit Statistics ◽  
Alternative Activities ◽  
Accessibility Measure ◽  
Better Than

This paper compares the relative performance of different measures of accessibility in relevant models. Specifically, the authors formulated three measures of accessibility: gravity-based accessibility, an aggregate measure of potential; trip-based accessibility, a disaggregate, utility-based measure of the value of travel alternatives; and activity-based accessibility, a theoretically richer disaggregate, utility-based measure of the value of alternative activities (including travel). These accessibility measures were used as explanatory variables in household vehicle ownership models and real estate market price models, comparing the explanatory power of each accessibility measure in each model as expressed by the confidence in the coefficient estimates and captured by the models’ goodness-of-fit statistics. It was found that trip-based accessibility best represents preferences for accessibility in both vehicle ownership decisions and property valuations. This supports the theoretical value of disaggregate, utility-based accessibility measures over aggregate, potential-based measures. The fact that trip-based measures perform better than activity-based accessibility measures underscores several empirical and technical limitations. Finally, the authors noted that accurately representing accessibility preferences requires congruence between the granularity of the accessibility measure and that of the explained behavior. This emphasizes the importance of understanding what accessibility measures actually capture and ensuring that they align with the analysis purpose.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

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