Modified information criteria for a uniform approximate equivalence of probability distributions

1986 ◽  
Vol 38 (2) ◽  
pp. 205-222
Author(s):  
T Matsunawa
Keyword(s):  
Probability Distributions ◽  
Information Criteria ◽  
Modified Information Criteria

scholarly journals An Exponentiated Odd Lindley Inverse Exponential Distribution and its Application to Infant Mortality and HIV Transmission Rates in Nigeria

2021 ◽  
pp. 12-30
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Gerald Ikechukwu Onwuka ◽  
Bassa Shiwaye Yakura ◽  
Hassan Allahde
Keyword(s):  
Infant Mortality ◽  
Exponential Distribution ◽  
Hiv Transmission ◽  
Transmission Rate ◽  
Probability Distributions ◽  
Real Life ◽  
Information Criteria ◽  
Infant Mortality Rate ◽  
Unknown Parameters ◽  
Inverse Exponential Distribution

Recently, researchers have shown much interest in developing new continuous probability distributions by adding one or two parameter(s) to the some existing baseline distributions. This act has been beneficial to the field of statistical theory especially in modeling of real life situations. Also, the exponentiated family as used in developing new distributions is an efficient method proposed and studied for defining more flexible continuous probability distributions for modeling real life data. In this study, the method of exponentiation has been used to develop a new distribution called “Exponentiated odd Lindley inverse exponential distribution”. Some properties of the proposed distribution and estimation of its unknown parameters has been done using the method of maximum likelihood estimation and its application to real life datasets. The new model has been applied to infant mortality rate and mother-to-child HIV transmission rate. The results of these two applications reveal that the proposed model is a better model compared to the other fitted existing models by some selection information criteria.

scholarly journals Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 55
Author(s):  
Vytaras Brazauskas ◽  
Sahadeb Upretee
Keyword(s):  
Value At Risk ◽  
Goodness Of Fit ◽  
Risk Measures ◽  
Probability Distributions ◽  
Simulated Data ◽  
Information Criteria ◽  
Asymptotic Distributions ◽  
Parametric Estimation ◽  
Goodness Of Fit Tests ◽  
Transfer Strategies

Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as in pricing of extreme events, developing reserve estimates, designing risk transfer strategies, and allocating capital. In this paper, we present the empirical nonparametric and two types of parametric estimators of quantiles at various levels. For parametric estimation, we employ the maximum likelihood and percentile-matching approaches. Asymptotic distributions of all the estimators under consideration are derived when data are left-truncated and right-censored, which is a typical loss variable modification in insurance. Then, we construct relative efficiency curves (REC) for all the parametric estimators. Specific examples of such curves are provided for exponential and single-parameter Pareto distributions for a few data truncation and censoring cases. Additionally, using simulated data we examine how wrong quantile estimates can be when one makes incorrect modeling assumptions. The numerical analysis is also supplemented with standard model diagnostics and validation (e.g., quantile-quantile plots, goodness-of-fit tests, information criteria) and presents an example of when those methods can mislead the decision maker. These findings pave the way for further work on RECs with potential for them being developed into an effective diagnostic tool in this context.

scholarly journals Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

2021 ◽  
Author(s):  
C Massiot ◽  
John Townend ◽  
A Nicol ◽  
DD McNamara
Keyword(s):  
Probability Distributions ◽  
Likelihood Estimation ◽  
Information Criterion ◽  
Geothermal Field ◽  
Information Criteria ◽  
Clustering Methods ◽  
Agglomerative Clustering ◽  
Data Set ◽  
Data Points ◽  
Borehole Televiewer

©2017. American Geophysical Union. All Rights Reserved. Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one-dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K-means, fuzzy K-means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high-temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

scholarly journals Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

2021 ◽  
Author(s):  
C Massiot ◽  
John Townend ◽  
A Nicol ◽  
DD McNamara
Keyword(s):  
Probability Distributions ◽  
Likelihood Estimation ◽  
Information Criterion ◽  
Geothermal Field ◽  
Information Criteria ◽  
Clustering Methods ◽  
Agglomerative Clustering ◽  
Data Set ◽  
Data Points ◽  
Borehole Televiewer

©2017. American Geophysical Union. All Rights Reserved. Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one-dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K-means, fuzzy K-means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high-temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

scholarly journals Kumaraswamy-Janardan Distribution: A Generalized Janardan Distribution with Application to Real Data

2021 ◽  
pp. 111-122
Author(s):  
Nelson Doe Dzivor ◽  
Henry Otoo ◽  
Eric Neebo Wiah
Keyword(s):  
Density Function ◽  
Hazard Rate ◽  
Probability Distributions ◽  
Real Data ◽  
Moment Generating Function ◽  
Rate Function ◽  
Information Criteria ◽  
Cumulative Density Function ◽  
Baseline Model ◽  
Generalized Distribution

The quest to improve on flexibility of probability distributions motivated this research. Four-parameter Janardan generalized distribution known as Kumaraswamy-Janardan distribution is proposed through method of parameterization and studied. The probability density function, cumulative density function, survival rate function as well as hazard rate function of the distribution are established. Statistical properties such as moments, moment generating function as well as maximum likelihood of the model are discussed. The parameters are estimated using the simulated annealing optimization algorithm.   Flexibility of the model in comparison with the baseline model as well as other competing sub-models is verified using Akaike Information Criteria (AIC). The model is tested with real data and is proven to be more flexible in fitting real data than any of its sub-models considered. 

Augmented Dickey-Fuller Test and the Lag Length Selection Problem

2011 ◽  
Vol 130-134 ◽  
pp. 3019-3022 ◽  
Author(s):  
Lu Deng
Keyword(s):  
Information Criteria ◽  
Selection Problem ◽  
Selection Methods ◽  
Leg Length ◽  
Selection Models ◽  
Proper Size ◽  
Augmented Dickey Fuller ◽  
Modified Information Criteria ◽  
Adf Test

Many studies indicated that ADF test is very sensitive to different leg length selection models. Based on Hall, and Ng, Perron’s works, this article simulates a more general ARIMA(0,1,q) process and compares the influence of different selection methods to the size and power of the ADF test. Finally, it is proved that the Modified Information Criteria always shows a more proper size and the General to Special Criteria has more robust ADF test properties.

scholarly journals The impacts of climate change on rainfall modeling in the Pantanal of Mato Grosso do Sul

2021 ◽  
Vol 43 ◽  
pp. e55112
Author(s):  
Ivana Pobocikova ◽  
Amaury de Souza ◽  
Marcel Carvalho Abreu ◽  
José Francisco de Oliveira-Júnior ◽  
Cícero Manoel dos Santos ◽  
...  
Keyword(s):  
Lognormal Distribution ◽  
Probability Distributions ◽  
Information Criteria ◽  
Rainfall Data ◽  
Coefficient Of Determination ◽  
Annual Rainfall ◽  
Distribution Models ◽  
Mato Grosso ◽  
Rainy Period ◽  
Mato Grosso Do Sul

The most significant and influential meteorological element in environmental conditions and human activities is precipitation. The objective of this study was to adjust eight probability distributions to monthly, seasonal and annual rainfall data in the Pantanal of Mato Grosso do Sul, Brazil, using a time series of data (1983-2013) by the National Meteorological Water Agency (ANA). The performance evaluation of different probability distribution models was assessed by the quality of fit of the selected probability distributions for precipitation data. Quality tests as chi-square, Kolmogorov-Smirnov (KS) and Anderson-Darling (AD), the information criteria as Akaike (AIC) and the Bayesian criterion (BIC) were used. Then the mean root square error (RMSE) and the coefficient of determination (R2) were applied. The analyzes were made monthly, annually and by seasons. The 3-parameter Lognormal distribution performs the best for all twelve months and provides the best-fit to the monthly rainfall data. Thus characterizing a dry period that runs from May to September and a rainy period between the months of October and April, it was observed that the 3-parameter Lognormal distribution has best adjustment for spring and summer, and for winter and autumn the 2-parameter Gamma and 3-parameter Gamma distribution performed better. For annual observations, the function that best fits is 3-parameter Weibull distribution.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

An Accelerated Cue Combination Principle Accounts for Multi-cue Depth Perception

2020 ◽  
Vol 3 (1) ◽  
pp. 10501-1-10501-9
Author(s):  
Christopher W. Tyler
Keyword(s):  
Belief Propagation ◽  
Probability Distributions ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Fusion Model ◽  
Cue Combination ◽  
Depth Estimate ◽  
Appropriate Behavior ◽  
Depth Cues ◽  
Bayesian Averaging

Abstract For the visual world in which we operate, the core issue is to conceptualize how its three-dimensional structure is encoded through the neural computation of multiple depth cues and their integration to a unitary depth structure. One approach to this issue is the full Bayesian model of scene understanding, but this is shown to require selection from the implausibly large number of possible scenes. An alternative approach is to propagate the implied depth structure solution for the scene through the “belief propagation” algorithm on general probability distributions. However, a more efficient model of local slant propagation is developed as an alternative.The overall depth percept must be derived from the combination of all available depth cues, but a simple linear summation rule across, say, a dozen different depth cues, would massively overestimate the perceived depth in the scene in cases where each cue alone provides a close-to-veridical depth estimate. On the other hand, a Bayesian averaging or “modified weak fusion” model for depth cue combination does not provide for the observed enhancement of perceived depth from weak depth cues. Thus, the current models do not account for the empirical properties of perceived depth from multiple depth cues.The present analysis shows that these problems can be addressed by an asymptotic, or hyperbolic Minkowski, approach to cue combination. With appropriate parameters, this first-order rule gives strong summation for a few depth cues, but the effect of an increasing number of cues beyond that remains too weak to account for the available degree of perceived depth magnitude. Finally, an accelerated asymptotic rule is proposed to match the empirical strength of perceived depth as measured, with appropriate behavior for any number of depth cues.

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