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 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 On the control of the difference between two Brownian motions: a dynamic copula approach

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Thomas Deschatre
Keyword(s):  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Gaussian Copula ◽  
Brownian Motions ◽  
Dynamic Copula ◽  
Copula Approach ◽  
The Difference ◽  
The Right

AbstractWe propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range of possible values for is the same for Markovian pairs and all pairs of Brownian motions, that is with φ being the cumulative distribution function of a standard Gaussian random variable.

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 A Load-Share Reliability Model under the Changeable Piecewise Smooth Load

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Sergey V. Gurov ◽  
Lev V. Utkin
Keyword(s):  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Continuous Functions ◽  
Piecewise Smooth ◽  
Cumulative Distribution ◽  
Residual Lifetime ◽  
Time To Failure ◽  
Reliability Model ◽  
Piecewise Constant ◽  
Proposed Model

A new load-share reliability model of systems under the changeable load is proposed in the paper. It is assumed that the load is a piecewise smooth function which can be regarded as an extension of the piecewise constant and continuous functions. The condition of the residual lifetime conservation, which means continuity of a cumulative distribution function of time to failure, is accepted in the proposed model. A general algorithm for computing reliability measures is provided. Simple expressions for determining the survivor functions under assumption of the Weibull probability distribution of time to failure are given. Various numerical examples illustrate the proposed model by different forms of the system load and different probability distributions of time to failure.

scholarly journals Closed form expressions for moments of the beta Weibull distribution

2011 ◽  
Vol 83 (2) ◽  
pp. 357-373 ◽  
Author(s):  
Gauss M Cordeiro ◽  
Alexandre B Simas ◽  
Borko D Stošic
Keyword(s):  
Weibull Distribution ◽  
Closed Form ◽  
Cumulative Distribution Function ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Set ◽  
Expected Information ◽  
Beta Weibull Distribution

The beta Weibull distribution was first introduced by Famoye et al. (2005) and studied by these authors and Lee et al. (2007). However, they do not give explicit expressions for the moments. In this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. We also obtain expansions for the cumulative distribution function and Rényi entropy. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. We also demonstrate the usefulness of this distribution on a real data set.

The joint asymptotic distribution of the k-smallest sample spacings

1969 ◽  
Vol 6 (02) ◽  
pp. 442-448
Author(s):  
Lionel Weiss
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Open Interval ◽  
Cumulative Distribution ◽  
The Right ◽  
Sample Spacings ◽  
Independent Identically Distributed

Suppose Q 1 ⋆, … Q n ⋆ are independent, identically distributed random variables, each with probability density function f(x), cumulative distribution function F(x), where F(1) – F(0) = 1, f(x) is continuous in the open interval (0, 1) and continuous on the right at x = 0 and on the left at x = 1, and there exists a positive C such that f(x) > C for all x in (0, l). f(0) is defined as f(0+), f(1) is defined as f(1–).

scholarly journals Product of κ-μ and α-μ Distributions and Their Composite Fading Distributions

2021 ◽  
Author(s):  
He Huang ◽  
Chaowei Yuan
Keyword(s):  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Total Power ◽  
The Novel ◽  
Mathematical Software ◽  
Composite Fading ◽  
Software Packages ◽  
Study Product ◽  
Close Form ◽  
Probability Density Function Pdf

In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-μ fading distribution and α-μ fading distribution is considered. The novel exact series formulas for the product of two i.n.i.d. fading distributions κ-μ and α-μ are derived instead of Fox H-function to solve the problem that Fox H function with multiple RVs cannot be implemented in professional mathematical software packages as MATHEMATICA and MAPLE. Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) are deduced to represent provided product expressions and generalized composite multipath shadowing models. At last, these analytical results are validated with Monte Carlo simulations, it shows that for provided κ-μ/α-μ model nonlinear parameter has more important influence than multipath component in PDF and CDF when the ratio between the total power of the dominant components and<br>the total power of the scattered waves is same. <br>

scholarly journals The tenets of indirect inference in Bayesian models

2021 ◽  
Author(s):  
Dmytro Perepolkin ◽  
Benjamin Goodrich ◽  
Ullrika Sahlin
Keyword(s):  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Bayesian Models ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Indirect Inference ◽  
Root Finding ◽  
Sampling Distributions ◽  
Definition Of

This paper extends the application of Bayesian inference to probability distributions defined in terms of its quantile function. We describe the method of *indirect likelihood* to be used in the Bayesian models with sampling distributions which lack an explicit cumulative distribution function. We provide examples and demonstrate the equivalence of the "quantile-based" (indirect) likelihood to the conventional "density-defined" (direct) likelihood. We consider practical aspects of the numerical inversion of quantile function by root-finding required by the indirect likelihood method. In particular, we consider a problem of ensuring the validity of an arbitrary quantile function with the help of Chebyshev polynomials and provide useful tips and implementation of these algorithms in Stan and R. We also extend the same method to propose the definition of an *indirect prior* and discuss the situations where it can be useful

NONPARAMETRIC KERNEL DISTRIBUTION FUNCTION ESTIMATION NEAR ENDPOINTS

2021 ◽  
Vol 10 (12) ◽  
pp. 3679-3697
Author(s):  
N. Almi ◽  
A. Sayah
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Kernel Estimator ◽  
Real Data ◽  
Cumulative Distribution ◽  
Function Estimation ◽  
Distribution Function Estimation ◽  
The Right ◽  
Nonparametric Kernel ◽  
Better Than

In this paper, two kernel cumulative distribution function estimators are introduced and investigated in order to improve the boundary effects, we will restrict our attention to the right boundary. The first estimator uses a self-elimination between modify theoretical Bias term and the classical kernel estimator itself. The basic technique of construction the second estimator is kind of a generalized reflection method involving reflection a transformation of the observed data. The theoretical properties of our estimators turned out that the Bias has been reduced to the second power of the bandwidth, simulation studies and two real data applications were carried out to check these phenomena and are conducted that the proposed estimators are better than the existing boundary correction methods.

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