BOUNDS ON EXTROPY WITH VARIATIONAL DISTANCE CONSTRAINT

2018 ◽  
Vol 33 (2) ◽  
pp. 186-204 ◽  
Author(s):  
Jianping Yang ◽  
Wanwan Xia ◽  
Taizhong Hu
Keyword(s):  
Probability Distribution ◽  
Confidence Interval ◽  
Upper Bound ◽  
Probability Distributions ◽  
Analytic Formula ◽  
Distance Constraint ◽  
Variation Distance ◽  
The Difference ◽  
Variational Distance

The relation between extropy and variational distance is studied in this paper. We determine the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution, obtain the tightest upper bound on the difference of extropies of any two probability distributions subject to the variational distance constraint, and establish an analytic formula for the confidence interval of an extropy. Such a study parallels to that of Ho and Yeung [3] concerning entropy. However, the proofs of the main results in this paper are different from those in Ho and Yeung [3]. In fact, our arguments can simplify several proofs in Ho and Yeung [3].

scholarly journals Accuracy of Approximation for Discrete Distributions

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Tamás F. Móri
Keyword(s):  
Total Variation ◽  
Generating Functions ◽  
Probability Distributions ◽  
Discrete Distributions ◽  
Discrete Probability ◽  
Order Of Magnitude ◽  
Variation Distance ◽  
The Difference ◽  
Discrete Probability Distributions ◽  
Accuracy Of Approximation

The paper is a contribution to the problem of estimating the deviation of two discrete probability distributions in terms of the supremum distance between their generating functions over the interval [0,1]. Deviation can be measured by the difference of the kth terms or by total variation distance. Our new bounds have better order of magnitude than those proved previously, and they are even sharp in certain cases.

scholarly journals LONG TERMS AND READABILITY OF PHYSICS SCHOOL TEXT

2017 ◽  
Vol 5 ◽  
pp. 815-819
Author(s):  
Ivana Ĺ korecová ◽  
Aba Teleki ◽  
Ľubomír Zelenický
Keyword(s):  
Probability Distribution ◽  
Strong Correlation ◽  
Test Scores ◽  
Probability Distributions ◽  
Survival Function ◽  
Survival Functions ◽  
School Text ◽  
The Difference ◽  
Random Fluctuations

This article presents a comparison of two physics school texts from the perspective of readability and use of specific terms. The study uses the survival function to associate the readability of physics school text to the length of terms used in the text. First, the study compares the survival functions of two full texts and that of the terms in these texts, and then analyzes the associated relative readability. Next, the results of two cloze tests involving 150 students are compared. The last step investigates the randomness of the differences between the results. The results show a strong correlation between the test scores and the probability distributions of terms used in the school texts. The difference between the probability distribution of the compared texts corresponds with the differences between the appropriate survival functions, where random fluctuations in the frequency of terms are suppressed.

scholarly journals Relationship among Continuous Probability Distributions and Interpolation

2021 ◽  
pp. 196-210
Author(s):  
Kelachi P. Enwere ◽  
Uchenna P. Ogoke
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Linear Interpolation ◽  
Data Set ◽  
Statistical Probability ◽  
Practical Applications ◽  
Gamma Distributions ◽  
Chi Squared ◽  
Interpolation Techniques ◽  
The Difference

Aims: The Study seeks to determine the relationship that exists among Continuous Probability Distributions and the use of Interpolation Techniques to estimate unavailable but desired value of a given probability distribution. Study Design: Statistical Probability tables for Normal, Student t, Chi-squared, F and Gamma distributions were used to compare interpolated values with statistical tabulated values. Charts and Tables were used to represent the relationships among the five probability distributions. Methodology: Linear Interpolation Technique was employed to interpolate unavailable but desired values so as to obtain approximate values from the statistical tables. The data were analyzed for interpolation of unavailable but desired values at 95% a-level from the five continuous probability distribution. Results: Interpolated values are as close as possible to the exact values and the difference between the exact value and the interpolated value is not pronounced. The table and chart established showed that relationships do exist among the Normal, Student-t, Chi-squared, F and Gamma distributions. Conclusion: Interpolation techniques can be applied to obtain unavailable but desired information in a data set. Thus, uncertainty found in a data set can be discovered, then analyzed and interpreted to produce desired results. However, understanding of how these probability distributions are related to each other can inform how best these distributions can be used interchangeably by Statisticians and other Researchers who apply statistical methods employed in practical applications.

scholarly journals Significant Associations of lncRNA H19 Genotypes with Susceptibility to Childhood Leukemia in Taiwan

2021 ◽  
Vol 14 (3) ◽  
pp. 235
Author(s):  
Jen-Sheng Pei ◽  
Chao-Chun Chen ◽  
Wen-Shin Chang ◽  
Yun-Chi Wang ◽  
Jaw-Chyun Chen ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Childhood Leukemia ◽  
Healthy Controls ◽  
Nucleotide Polymorphisms ◽  
Wild Type ◽  
Single Nucleotide ◽  
Genotypic Distribution ◽  
Heterozygous Variant ◽  
Significant Difference ◽  
The Difference

The purpose of our study was to investigate whether genetic variations in lncRNA H19 were associated with susceptibility to childhood leukemia. Two hundred and sixty-six childhood leukemia patients and 266 healthy controls were enrolled in Taiwan, and two single nucleotide polymorphisms (SNPs), rs2839698 and rs217727, in H19 were genotyped and analyzed. There was a significant difference in the genotypic distribution of rs2839698 between patients and healthy controls (p = 0.0277). Compared to the wild-type CC genotype, the heterozygous variant CT and homozygous variant TT genotypes were associated with significantly increased risks of childhood leukemia with an adjusted odd ratio (OR) of 1.46 (95% confidence interval (CI), 1.08–2.14, p = 0.0429) and 1.94 (95%CI, 1.15–3.31, p = 0.0169), respectively (pfor tread = 0.0277). The difference in allelic frequencies between childhood leukemia patients and controls was also significant (T versus C, adjusted OR = 1.53, 95%CI, 1.13–1.79, p = 0.0077). There were no significant differences in the genotypic and allelic distributions of rs217727 between cases and controls. Interestingly, the average level of H19 rs2839698 was statistically significantly higher for patients with CT and TT genotypes than from those with the CC genotype (p < 0.0001). Our results indicate that H19 SNP rs2839698, but not rs217727, may serve as a novel susceptibility marker for childhood leukemia.

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

WIGNER FUNCTION OF PULSED FIELDS RECONSTRUCTED BY DIRECT DETECTION

2011 ◽  
Vol 09 (supp01) ◽  
pp. 39-47
Author(s):  
ALESSIA ALLEVI ◽  
MARIA BONDANI ◽  
ALESSANDRA ANDREONI
Keyword(s):  
Probability Distribution ◽  
Wigner Function ◽  
Beam Splitter ◽  
Direct Detection ◽  
Probability Distributions ◽  
Linear Regime ◽  
Wigner Functions ◽  
Intensity Measurements ◽  
Pulsed Fields

We present the experimental reconstruction of the Wigner function of some optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. The signal state is mixed at a beam-splitter with a set of coherent probes of known complex amplitudes and the probability distribution of the detected photons is measured. The Wigner function is given by a suitable sum of these probability distributions measured for different values of the probe. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.

Analysis of Magnitude and Frequency of Floods in the Damanganga Basin: Western India

2021 ◽  
Vol 5 (1) ◽  
pp. 1-11
Author(s):  
Vitthal Anwat ◽  
Pramodkumar Hire ◽  
Uttam Pawar ◽  
Rajendra Gunjal
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Western India ◽  
Type I ◽  
Return Periods ◽  
Pearson Type ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

Flood Frequency Analysis (FFA) method was introduced by Fuller in 1914 to understand the magnitude and frequency of floods. The present study is carried out using the two most widely accepted probability distributions for FFA in the world namely, Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). The Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) methods were used to select the most suitable probability distribution at sites in the Damanganga Basin. Moreover, discharges were estimated for various return periods using GEVI and LP-III. The recurrence interval of the largest peak flood on record (Qmax) is 107 years (at Nanipalsan) and 146 years (at Ozarkhed) as per LP-III. Flood Frequency Curves (FFC) specifies that LP-III is the best-fitted probability distribution for FFA of the Damanganga Basin. Therefore, estimated discharges and return periods by LP-III probability distribution are more reliable and can be used for designing hydraulic structures.

Analysis and Synthesis of Mechanical Error in Universal Joints

1990 ◽  
Author(s):  
J. L. Cagney ◽  
S. S. Rao
Keyword(s):  
Probability Distribution ◽  
Real World ◽  
Probability Distributions ◽  
Manufacturing Cost ◽  
Universal Joint ◽  
Accuracy Requirement ◽  
Output Error ◽  
Manufacturing Errors ◽  
Analysis And Synthesis ◽  
Limiting Value

Abstract The modeling of manufacturing errors in mechanisms is a significant task to validate practical designs. The use of probability distributions for errors can simulate manufacturing variations and real world operations. This paper presents the mechanical error analysis of universal joint drivelines. Each error is simulated using a probability distribution, i.e., a design of the mechanism is created by assigning random values to the errors. Each design is then evaluated by comparing the output error with a limiting value and the reliability of the universal joint is estimated. For this, the design is considered a failure whenever the output error exceeds the specified limit. In addition, the problem of synthesis, which involves the allocation of tolerances (errors) for minimum manufacturing cost without violating a specified accuracy requirement of the output, is also considered. Three probability distributions — normal, Weibull and beta distributions — were used to simulate the random values of the errors. The similarity of the results given by the three distributions suggests that the use of normal distribution would be acceptable for modeling the tolerances in most cases.

Field-theoretic density estimation for biological sequence space with applications to 5′ splice site diversity and aneuploidy in cancer

2021 ◽  
Vol 118 (40) ◽  
pp. e2025782118
Author(s):  
Wei-Chia Chen ◽  
Juannan Zhou ◽  
Jason M. Sheltzer ◽  
Justin B. Kinney ◽  
David M. McCandlish
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Density Estimation ◽  
Sequence Space ◽  
Chromosomal Abnormalities ◽  
Fundamental Problem ◽  
Probability Distributions ◽  
Biological Sequence ◽  
Point Estimates ◽  
Site Diversity

Density estimation in sequence space is a fundamental problem in machine learning that is also of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy (i.e., calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates). Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data are plentiful while still maintaining a conservative maximum entropy character in regions of sequence space where data are sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyperparameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5′ splice sites found in the human genome and to understand patterns of chromosomal abnormalities across human cancers.

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.

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