scholarly journals Probability Distributions for the Insight Toolkit

2006 ◽  
Author(s):  
James Miller
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Statistical Tests ◽  
Cumulative Distribution ◽  
Clinical Literature ◽  
Chi Squared ◽  
Mean And Variance ◽  
Function Inverse ◽  
Probability Density Function Pdf

Probability distributions are a key component of clinical research. One only has to make a cursory review of clinical literature to realize that nearly all clinical publications reference some sort of statistical test; be it t-test, chi-squared test, or F-test. In this paper, we describe an architecture for providing the Insight Toolkit with access to probability distributions. The architecture can support parametric and nonparametric probability distributions. Each distribution provides access to its probability density function (PDF), cumulative distribution function (CDF), inverse cumulative distribution function (inverse CDF), mean, and variance. These methods form the basis of statistical tests.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

scholarly journals Transmuted Probability Distributions: A Review

2020 ◽  
pp. 83-94
Author(s):  
Md. Mahabubur Rahman ◽  
Bander Al-Zahrani ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Functional Composition ◽  
Inverse Cumulative Distribution Function ◽  
Family Of Distributions

Transmutation is the functional composition of the cumulative distribution function (cdf) of one distribution with the inverse cumulative distribution function (quantile function) of another. Shaw and Buckley(2007), first apply this concept and introduced quadratic transmuted family of distributions. In this article, we have presented a review about the transmuted families of distributions. We have also listed the transmuted distributions, available in the literature along with some concluding remarks.

scholarly journals Bin-Free Fitting of Probability Distributions Emphasizing DNA Histograms

2017 ◽  
Author(s):  
Nash Rochman
Keyword(s):  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Cumulative Distribution ◽  
Data Set ◽  
Cell Synchronization ◽  
Approximate Probability ◽  
A Cell ◽  
The Right ◽  
Probability Density Function Pdf ◽  
Dna Histograms

AbstractIt is often challenging to find the right bin size when constructing a histogram to represent a noisy experimental data set. This problem is frequently faced when assessing whether a cell synchronization experiment was successful or not. In this case the goal is to determine whether the DNA content is best represented by a unimodal, indicating successful synchronization, or bimodal, indicating unsuccessful synchronization, distribution. This choice of bin size can greatly affect the interpretation of the results; however, it can be avoided by fitting the data to a cumulative distribution function (CDF). Fitting data to a CDF removes the need for bin size selection. The sorted data can also be used to reconstruct an approximate probability density function (PDF) without selecting a bin size. A simple CDF-based approach is presented and the benefits and drawbacks relative to usual methods are discussed.

scholarly journals Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves

2021 ◽  
Author(s):  
Hime Oliveira
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Number ◽  
Probability Distributions ◽  
Cumulative Distribution ◽  
Standard Normal Distribution ◽  
Space Filling ◽  
Space Filling Curves ◽  
Deterministic Sampling ◽  
Standard Normal

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

scholarly journals The Distribution of the Ratio of the Products of Two Independentα-μVariates and Its Application in the Performance Analysis of Relaying Communication Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ana Matović ◽  
Edis Mekić ◽  
Nikola Sekulović ◽  
Mihajlo Stefanović ◽  
Marija Matović ◽  
...  
Keyword(s):  
Distribution Function ◽  
Performance Analysis ◽  
Probability Density Function ◽  
Theoretical Analysis ◽  
Communication Systems ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Wireless Communication Systems ◽  
Multihop Wireless ◽  
Probability Density Function Pdf

We present novel general, simple, exact, and closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the ratio of the products of two independentα-μvariates, where all variates have identical values of alpha parameter. Obtained results are applied in analysis of multihop wireless communication systems in different fading transmission environments. The proposed theoretical analysis is also complemented by various graphically presented numerical results.

scholarly journals Stereological Analysis of the Statistical Distribution of the Size of Graphite Nodules in DI

2018 ◽  
Vol 925 ◽  
pp. 98-103
Author(s):  
Andriy A. Burbelko ◽  
Daniel Gurgul ◽  
Edward Guzik ◽  
Wojciech Kapturkiewicz
Keyword(s):  
Distribution Function ◽  
Cross Section ◽  
Cumulative Distribution Function ◽  
Length Distribution ◽  
Cumulative Distribution ◽  
Nucleation Kinetics ◽  
Distribution Law ◽  
Chord Length Distribution ◽  
Random Sections ◽  
Probability Density Function Pdf

The estimate of a distribution law of the nodule diameters in a volume of cast iron provides information about the graphite nucleation kinetics, and also about the crystallization kinetics. This information is essential for building more accurate mathematical models of the alloy crystallization. The mapping of a Cumulative Distribution Function (CDF3) of radii for graphite nodules in ductile iron is presented on the base of a Probability Density Function (PDF1) of the chord length distribution for random sections of the sample at the planar cross-section.

3-D Research about Walfisch-Bertoni Model

2013 ◽  
Vol 385-386 ◽  
pp. 1527-1530 ◽  
Author(s):  
Jie Chen ◽  
Dong Ya Shen ◽  
Na Yao ◽  
Ren Zhang
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Path Loss ◽  
Signal Propagation ◽  
Loss Probability ◽  
Cumulative Distribution ◽  
Diffraction Loss ◽  
Wireless Signal ◽  
Probability Density Function Pdf ◽  
Signal Field

Walfisch - Bertoni model is used to predict the average signal field intensity of the main street. The model considers the path loss of the free space, diffraction loss along the path, and the influence of the height of the building. There are six City parameters in Walfisch - Bertoni model influence communication quality. In this paper, the researches about path loss and its characteristics is under the case of considering two city parameters at the same time. Facts have proved that this case is more close to the actual that the wireless signal propagation environment. This paper mainly researched the path loss, probability density function (PDF) and cumulative distribution function (CDF) of the path loss.

scholarly journals On the Properties and Applications of Transmuted Odd Generalized Exponential-Exponential Distribution

2018 ◽  
pp. 1-14
Author(s):  
Jamila Abdullahi ◽  
Umar Kabir Abdullahi ◽  
Terna Godfrey Ieren ◽  
David Adugh Kuhe ◽  
Adamu Abubakar Umar
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Exponential Distribution ◽  
Cumulative Distribution Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution

This article proposed a new distribution referred to as the transmuted odd generalized exponential-exponential distribution (TOGEED) as an extension of the popular odd generalized exponential- exponential distribution by using the Quadratic rank transmutation map (QRTM) proposed and studied by [1]. Using the transmutation map, we defined the probability density function (pdf) and cumulative distribution function (cdf) of the transmuted odd generalized Exponential- Exponential distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Exponential distribution using a real life dataset.  

scholarly journals Evolution of bioacoustic correlometers: from setups for analysis of probability density function (PDF), cumulative distribution function (CDF), [spectral] entropy of signal (SE) & quality of masking noise (QMN) to palmtop-like pocket devices

2019 ◽  
Author(s):  
Oleg Gradov ◽  
Eugene Adamovich ◽  
Serge Pankratov
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Spectral Entropy ◽  
Masking Noise ◽  
Probability Density Function Pdf

Evolution of bioacoustic correlometers: from setups for analysis of probability density function (PDF), cumulative distribution function (CDF), [spectral] entropy of signal (SE) & quality of masking noise (QMN) to palmtop-like pocket devices Novel references:

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