USEFUL PROPERTIES OF THE MAJORITY BINOMIAL PROBABILITY FUNCTION

1961 ◽  
Author(s):  
Bobby L. Buchanan
Keyword(s):  
Probability Function ◽  
Binomial Probability

On the Distribution of Sum of Independent Positive Binomial Variables

1970 ◽  
Vol 13 (1) ◽  
pp. 151-152 ◽  
Author(s):  
J. C. Ahuja
Keyword(s):  
Power Series ◽  
Inversion Formula ◽  
Probability Function ◽  
Random Variables ◽  
Random Variable ◽  
Characteristic Functions ◽  
Binomial Probability ◽  
Generalized Power Series ◽  
Alternative Derivation ◽  
Image Position

Let X1, X2, …, Xn be n independent and identically distributed random variables having the positive binomial probability function1where 0 < p < 1, and T = {1, 2, …, N}. Define their sum as Y=X1 + X2 + … +Xn. The distribution of the random variable Y has been obtained by Malik [2] using the inversion formula for characteristic functions. It appears that his result needs some correction. The purpose of this note is to give an alternative derivation of the distribution of Y by applying one of the results, established by Patil [3], for the generalized power series distribution.

Modification of Pascal's triangle for calculating size distributions in polymers

1970 ◽  
Vol 48 (9) ◽  
pp. 1432-1435 ◽  
Author(s):  
S. G. Whiteway
Keyword(s):  
Size Distribution ◽  
Probability Function ◽  
Molecular Size ◽  
Size Distributions ◽  
Binomial Probability ◽  
Alternative Concept ◽  
Pascal’S Triangle ◽  
All Solutions ◽  
Molecular Size Distribution ◽  
Pascal's Triangle

Pascal's triangle, which is well known to yield all solutions to the factorial part of the Bernoulli binomial probability function, is modified to yield the correct factorial term in expressions for the molecular size distribution in polymers. This approach provides an alternative concept of the meaning of these factorial numbers.

Development of Statistical Models to Simulate the Testing of Farmers Stock Peanuts for Aflatoxin Using Visual, Thin Layer Chromatography, and Minicolumn Methods1

1985 ◽  
Vol 12 (2) ◽  
pp. 94-98 ◽  
Author(s):  
T. B Whitaker ◽  
J. W Dickens ◽  
V Chew
Keyword(s):  
Thin Layer ◽  
Thin Layer Chromatography ◽  
Statistical Models ◽  
Probability Function ◽  
Negative Binomial ◽  
Published Data ◽  
Test Results ◽  
Binomial Probability ◽  
Layer Chromatography ◽  
Good Agreement

Abstract The negative binomial probability function was used to model the distribution of sample aflatoxin test results when replicated grade samples from farmers stock peanuts are analyzed by thin layer chromatography and minicolumn methods. The Poisson probability funtion was used to model the distribution of the number of kernels with visible Aspergillus flavus growth found in replicated grade samples of farmers stock peanuts when the visible A. flavus method is used. The probabilities of accepting a lot of farmers stock peanuts with given aflatoxin concentrations when using a 465-g grade sample and 2 different accept/reject levels were predicted with the models and compared to observed acceptance probabilities computed from previously published data for each of the 3 methods. The comparisons showed good agreement between the predicted acceptance probabilities and the observed acceptance probabilities.

Random Forest Refinement of Pairwise Potentials for Protein-ligand Decoy Detection

2019 ◽  
Author(s):  
Jun Pei ◽  
Zheng Zheng ◽  
Hyunji Kim ◽  
Lin Song ◽  
Sarah Walworth ◽  
...  
Keyword(s):  
Machine Learning ◽  
Random Forest ◽  
Probability Function ◽  
Pair Potential ◽  
Scoring Function ◽  
Stable Structure ◽  
Scoring Functions ◽  
Atom Pair ◽  
Data Set ◽  
Atom Pairs

An accurate scoring function is expected to correctly select the most stable structure from a set of pose candidates. One can hypothesize that a scoring function’s ability to identify the most stable structure might be improved by emphasizing the most relevant atom pairwise interactions. However, it is hard to evaluate the relevant importance for each atom pair using traditional means. With the introduction of machine learning methods, it has become possible to determine the relative importance for each atom pair present in a scoring function. In this work, we use the Random Forest (RF) method to refine a pair potential developed by our laboratory (GARF6) by identifying relevant atom pairs that optimize the performance of the potential on our given task. Our goal is to construct a machine learning (ML) model that can accurately differentiate the native ligand binding pose from candidate poses using a potential refined by RF optimization. We successfully constructed RF models on an unbalanced data set with the ‘comparison’ concept and, the resultant RF models were tested on CASF-2013.5 In a comparison of the performance of our RF models against 29 scoring functions, we found our models outperformed the other scoring functions in predicting the native pose. In addition, we used two artificial designed potential models to address the importance of the GARF potential in the RF models: (1) a scrambled probability function set, which was obtained by mixing up atom pairs and probability functions in GARF, and (2) a uniform probability function set, which share the same peak positions with GARF but have fixed peak heights. The results of accuracy comparison from RF models based on the scrambled, uniform, and original GARF potential clearly showed that the peak positions in the GARF potential are important while the well depths are not. <br>

scholarly journals Time and Life in the Relational Universe: Prolegomena to an Integral Paradigm of Natural Philosophy

Philosophies ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 30 ◽  
Author(s):  
Abir Igamberdiev
Keyword(s):  
Probability Function ◽  
Natural Philosophy ◽  
Natural World ◽  
Spatiotemporal Structure ◽  
Internal Logic ◽  
Decision Making System ◽  
Relational Domains ◽  
Relational Order ◽  
Infinite Set ◽  
The Universe

Relational ideas for our description of the natural world can be traced to the concept of Anaxagoras on the multiplicity of basic particles, later called “homoiomeroi” by Aristotle, that constitute the Universe and have the same nature as the whole world. Leibniz viewed the Universe as an infinite set of embodied logical essences called monads, which possess inner view, compute their own programs and perform mathematical transformations of their qualities, independently of all other monads. In this paradigm, space appears as a relational order of co-existences and time as a relational order of sequences. The relational paradigm was recognized in physics as a dependence of the spatiotemporal structure and its actualization on the observer. In the foundations of mathematics, the basic logical principles are united with the basic geometrical principles that are generic to the unfolding of internal logic. These principles appear as universal topological structures (“geometric atoms”) shaping the world. The decision-making system performs internal quantum reduction which is described by external observers via the probability function. In biology, individual systems operate as separate relational domains. The wave function superposition is restricted within a single domain and does not expand outside it, which corresponds to the statement of Leibniz that “monads have no windows”.

scholarly journals Estimating a resource selection function with line transect sampling

2002 ◽  
Vol 6 (4) ◽  
pp. 213-228 ◽  
Author(s):  
Bryan F. J. Manly
Keyword(s):  
Resource Selection ◽  
Probability Function ◽  
Resource Selection Function ◽  
Line Transect ◽  
Selection Function ◽  
Line Transect Sampling ◽  
Selection Probability ◽  
Transect Sampling ◽  
Conditional Maximum ◽  
Habitat Variables

A resource selection probability function is a function that gives the prob- ability that a resource unit (e.g., a plot of land) that is described by a set of habitat variables X1 to Xp will be used by an animal or group of animals in a certain period of time. The estimation of a resource selection function is usually based on the comparison of a sample of resource units used by an animal with a sample of the resource units that were available for use, with both samples being assumed to be effectively randomly selected from the relevant populations. In this paper the possibility of using a modified sampling scheme is examined, with the used units obtained by line transect sampling. A logistic regression type of model is proposed, with estimation by conditional maximum likelihood. A simulation study indicates that the proposed method should be useful in practice.

SOME TESTS OF BINOMIAL PROBABILITY ASSESSMENTS

1978 ◽  
Vol 9 (4) ◽  
pp. 564-576
Author(s):  
William S. Peters
Keyword(s):  
Binomial Probability
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