scholarly journals Externally studentized normal midrange distribution

2017 ◽  
Vol 41 (4) ◽  
pp. 378-389
Author(s):  
Ben Dêivide de Oliveira Batista ◽  
Daniel Furtado Ferreira ◽  
Lucas Monteiro Chaves
Keyword(s):  
Probability Density ◽  
Degrees Of Freedom ◽  
R Package ◽  
Cumulative Distribution ◽  
R Software ◽  
Studentized Range ◽  
Quantile Functions ◽  
Legendre Quadrature ◽  
Raphson Method ◽  
New Distribution

ABSTRACT The distribution of externally studentized midrange was created based on the original studentization procedures of Student and was inspired in the distribution of the externally studentized range. The large use of the externally studentized range in multiple comparisons was also a motivation for developing this new distribution. This work aimed to derive analytic equations to distribution of the externally studentized midrange, obtaining the cumulative distribution, probability density and quantile functions and generating random values. This is a new distribution that the authors could not find any report in the literature. A second objective was to build an R package for obtaining numerically the probability density, cumulative distribution and quantile functions and make it available to the scientific community. The algorithms were proposed and implemented using Gauss-Legendre quadrature and the Newton-Raphson method in R software, resulting in the SMR package, available for download in the CRAN site. The implemented routines showed high accuracy proved by using Monte Carlo simulations and by comparing results with different number of quadrature points. Regarding to the precision to obtain the quantiles for cases where the degrees of freedom are close to 1 and the percentiles are close to 100%, it is recommended to use more than 64 quadrature points.

scholarly journals On a new distribution based on the arccosine function

2021 ◽  
Author(s):  
Christophe Chesneau ◽  
Lishamol Tomy ◽  
Jiju Gillariose
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Power Functions ◽  
New Distribution

AbstractThis note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

scholarly journals Cylcop: An R Package for Circular-Linear Copulae with Angular Symmetry

2021 ◽  
Author(s):  
Florian H. Hodel ◽  
John R. Fieberg
Keyword(s):  
Probability Density ◽  
Discrete Time ◽  
Random Variables ◽  
R Package ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Animal Movements ◽  
Cumulative Distribution Functions ◽  
Model Animal

The cylcop package extends the copula package to allow modeling of correlated circular-linear random variables using copulae that are symmetric in the circular dimension. We present and derive several new circular-linear copulae with this property and demonstrate how they can be implemented in the cylcop package to model animal movements in discrete time. The package contains methods for estimating copulae parameters, plotting probability density and cumulative distribution functions, and simulating data.

scholarly journals BLACK HOLE EVAPORATION BASED UPON A q-DEFORMATION DESCRIPTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6039-6049 ◽  
Author(s):  
XIN ZHANG
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Radiation Spectrum ◽  
Correlation Effect ◽  
Space Time ◽  
Noncommutative Space ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation ◽  
Starting Point ◽  
New Distribution

A toy model based upon the q-deformation description for studying the radiation spectrum of black hole is proposed. The starting point is to make an attempt to consider the space–time noncommutativity in the vicinity of black hole horizon. We use a trick that all the space–time noncommutative effects are ascribed to the modification of the behavior of the radiation field of black hole and a kind of q-deformed degrees of freedom are postulated to mimic the radiation particles that live on the noncommutative space–time, meanwhile the background metric is preserved as usual. We calculate the radiation spectrum of Schwarzschild black hole in this framework. The new distribution deviates from the standard thermal spectrum evidently. The result indicates that some correlation effect will be introduced to the system if the noncommutativity is taken into account. In addition, an infrared cutoff of the spectrum is the prediction of the model.

3 Power and sample size for ABE in the 2× 2 design Here we give formulae for the calculation of the power of the TOST procedure assuming that there are in total n subjects in the 2× 2 trial. Suppose that the null hypotheses given below are to be tested using a 100(1 − α)% two-sided confidence interval and a power of (1 − β) is required to reject these hypotheses when they are false. H :µ ≤− ln 1.25 H :µ ≥ ln 1.25. Let us define x to be a random variable that has a noncentral t-distribution with df degrees of freedom and noncentrality parameter nc, i.e., x ∼ t(df,nc). The cumulative distribution function of x is defined as CDF(t,df,nc) = Pr(x≤ t). Assume that the power is to be calculated using log(AUC). If σ is the common within-subject variance for T and R for log(AUC), and n/2 subjects are allocated to each of the sequences RT and TR, then 1−β = CDF(t , df,nc )−CDF(t , df,nc ) (7.1) where √ n(log(µ )− log(0.8)) nc = 2σ √ n(log(µ )− log(1.25)) nc = 2σ √ (n− 2)(nc −nc = ) df 2t and t is the 100(1 − α)% point of the central t-distribution on n− 2 degrees of freedom. Some SAS code to calculate the power for an ABE 2 × 2 trial is given below, where the required input variables are α, σ value of the ratio µ and n, the total number of subjects in the trial.

2003 ◽  
pp. 361-361
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Degrees Of Freedom ◽  
Random Variable ◽  
Noncentrality Parameter ◽  
Cumulative Distribution ◽  
Total N ◽  
The Common ◽  
Input Variables ◽  
T Distribution

scholarly journals A Probability Density Function Generator Based on Deep Learning

2018 ◽  
Author(s):  
Chi-Hua Chen ◽  
Fangying Song ◽  
Feng-Jang Hwang ◽  
Ling Wu
Keyword(s):  
Deep Learning ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Real Data ◽  
Learning Model ◽  
Cumulative Distribution ◽  
Function Generator ◽  
Deep Learning Model

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

scholarly journals Identifying home locations in human mobility data: an open-source R package for comparison and reproducibility

2021 ◽  
Author(s):  
Qingqing Chen ◽  
Ate Poorthuis
Keyword(s):  
Software Package ◽  
Ad Hoc ◽  
Human Mobility ◽  
Building Blocks ◽  
R Package ◽  
Location Based Services ◽  
R Software ◽  
Mobility Data ◽  
Residential Population ◽  
Research Goal

Identifying meaningful locations, such as home or work, from human mobility data has become an increasingly common prerequisite for geographic research. Although location-based services (LBS) and other mobile technology have rapidly grown in recent years, it can be challenging to infer meaningful places from such data, which - compared to conventional datasets – can be devoid of context. Existing approaches are often developed ad-hoc and can lack transparency and reproducibility. To address this, we introduce an R software package for inferring home locations from LBS data. The package implements pre-existing algorithms and provides building blocks to make writing algorithmic ‘recipes’ more convenient. We evaluate this approach by analyzing a de-identified LBS dataset from Singapore that aims to balance ethics and privacy with the research goal of identifying meaningful locations. We show that ensemble approaches, combining multiple algorithms, can be especially valuable in this regard as the resulting patterns of inferred home locations closely correlate with the distribution of residential population. We hope this package, and others like it, will contribute to an increase in use and sharing of comparable algorithms, research code and data. This will increase transparency and reproducibility in mobility analyses and further the ongoing discourse around ethical big data research.

scholarly journals FIREcaller: Detecting Frequently Interacting Regions from Hi-C Data

2019 ◽  
Author(s):  
Cheynna Crowley ◽  
Yuchen Yang ◽  
Yunjiang Qiu ◽  
Benxia Hu ◽  
Armen Abnousi ◽  
...  
Keyword(s):  
Gene Regulation ◽  
Spatial Organization ◽  
R Package ◽  
Specific Gene ◽  
List Type ◽  
Cell Type ◽  
R Software ◽  
Computational Tools ◽  
Cell Type Specific ◽  
User Friendly

AbstractHi-C experiments have been widely adopted to study chromatin spatial organization, which plays an essential role in genome function. We have recently identified frequently interacting regions (FIREs) and found that they are closely associated with cell-type-specific gene regulation. However, computational tools for detecting FIREs from Hi-C data are still lacking. In this work, we present FIREcaller, a stand-alone, user-friendly R package for detecting FIREs from Hi-C data. FIREcaller takes raw Hi-C contact matrices as input, performs within-sample and cross-sample normalization, and outputs continuous FIRE scores, dichotomous FIREs, and super-FIREs. Applying FIREcaller to Hi-C data from various human tissues, we demonstrate that FIREs and super-FIREs identified, in a tissue-specific manner, are closely related to gene regulation, are enriched for enhancer-promoter (E-P) interactions, tend to overlap with regions exhibiting epigenomic signatures of cis-regulatory roles, and aid the interpretation or GWAS variants. The FIREcaller package is implemented in R and freely available at https://yunliweb.its.unc.edu/FIREcaller.Highlights– Frequently Interacting Regions (FIREs) can be used to identify tissue and cell-type-specific cis-regulatory regions.– An R software, FIREcaller, has been developed to identify FIREs and clustered FIREs into super-FIREs.

Quasi-Static Modelling and Computer Simulation of Hanging Cables on Robots

1994 ◽  
Author(s):  
Li-Ping Yang ◽  
Shin-Min Song
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Finite Segment ◽  
Revolute Joints ◽  
Highly Nonlinear ◽  
Finite Segment Method ◽  
Newton Raphson ◽  
Static Modelling ◽  
Parameter Perturbation Method ◽  
Raphson Method

Abstract This paper presents a computer method to simulate the quasi-static motion of hanging cables on robots. The shape of the flexible cable is changing during motion and the finite segment method is applied to determine its configuration. The cable is modeled as a series of rigid segments segments connected together through revolute joints in 2-D case and spherical joints in 3-D case. The elasticity of cable is represented by torsional springs at the joints. In both cases, a set of highly nonlinear equations are derived based on force equilibrium and the Newton-Raphson method is applied to calculate the solution. In order to assure convergence and improve computational efficiency, the parameter perturbation method is applied together with the Newton-Raphson method. Also, some computational strategies are developed to simplify the three dimensional problem. Finally, the developed methods are demonstrated in displaying the motion of a hanging cable which is attached to a revolute joint, a prismatic joint and a three degrees of freedom robot.

Fourier Transforms in Probability, Random Variables and Stochastic Processes

2009 ◽  
Author(s):  
Robert J Marks II
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Fourier Analysis ◽  
Stochastic Processes ◽  
Probability Density ◽  
Density Function ◽  
Fourier Transforms ◽  
Random Variables ◽  
Cumulative Distribution ◽  
The Face

In this Chapter, we present application of Fourier analysis to probability, random variables and stochastic processes [1089, 1097, 1387, 1329]. Arandom variable, X, is the assignment of a number to the outcome of a random experiment. We can, for example, flip a coin and assign an outcome of a heads as X = 1 and a tails X = 0. Often the number is equated to the numerical outcome of the experiment, such as the number of dots on the face of a rolled die or the measurement of a voltage in a noisy circuit. The cumulative distribution function is defined by FX(x) = Pr[X ≤ x]. (4.1) The probability density function is the derivative fX(x) = d /dxFX(x). Our treatment of random variables focuses on use of Fourier analysis. Due to this viewpoint, the development we use is unconventional and begins immediately in the next section with discussion of properties of the probability density function.

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