Some possible q-exponential type probability distribution in the non-extensive statistical physics

2016 ◽  
Vol 30 (22) ◽  
pp. 1650252 ◽  
Author(s):  
Won Sang Chung
Keyword(s):  
Probability Distribution ◽  
Exponential Type ◽  
Statistical Physics ◽  
Probability Distributions ◽  
Type I ◽  
Quantum Harmonic Oscillator ◽  
Text Type ◽  
First Order ◽  
Gibbs Entropy ◽  
Level Problem

In this paper, we present two exponential type probability distributions which are different from Tsallis’s case which we call Type I: one given by [Formula: see text] (Type IIA) and another given by [Formula: see text] (Type IIIA). Starting with the Boltzman–Gibbs entropy, we obtain the different probability distribution by using the Kolmogorov–Nagumo average for the microstate energies. We present the first-order differential equations related to Types I, II and III. For three types of probability distributions, we discuss the quantum harmonic oscillator, two-level problem and the spin-[Formula: see text] paramagnet.

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.

scholarly journals Rainfall models – a study over Gangtok

MAUSAM ◽  
2021 ◽  
Vol 61 (2) ◽  
pp. 225-228
Author(s):  
K. SEETHARAM
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Uniform Distribution ◽  
Probability Distribution Function ◽  
Null Hypothesis ◽  
Probability Distributions ◽  
Data Sets ◽  
Type I ◽  
Anderson Darling ◽  
Pearsonian Type

In this paper, the Pearsonian system of curves were fitted to the monthly rainfalls from January to December, in addition to the seasonal as well as annual rainfalls totalling to 14 data sets of the period 1957-2005 with 49 years of duration for the station Gangtok to determine the probability distribution function of these data sets. The study indicated that the monthly rainfall of July and summer monsoon seasonal rainfall did not fit in to any of the Pearsonian system of curves, but the monthly rainfalls of other months and the annual rainfalls of Gangtok station indicated to fit into Pearsonian type-I distribution which in other words is an uniform distribution. Anderson-Darling test was applied to for null hypothesis. The test indicated the acceptance of null-hypothesis. The statistics of the data sets and their probability distributions are discussed in this paper.

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 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.

Differential Credibility of Climate Modes in CMIP6

2021 ◽  
pp. 1
Author(s):  
Jacob Coburn ◽  
S.C. Pryor
Keyword(s):  
Southern Oscillation ◽  
Probability Distributions ◽  
Critical Role ◽  
Regional Scale ◽  
Southern Annular Mode ◽  
Climate Projections ◽  
Annular Mode ◽  
Climate Modes ◽  
First Order ◽  
Skill Scores

AbstractThis work quantitatively evaluates the fidelity with which the Northern Annular Mode (NAM), Southern Annular Mode (SAM), Pacific-North American pattern (PNA), El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Oscillation (AMO) and the first-order mode interactions are represented in Earth System Model (ESM) output from the CMIP6 archive. Several skill metrics are used as part of a differential credibility assessment (DCA) of both spatial and temporal characteristics of the modes across ESMs, ESM families and specific ESM realizations relative to ERA5. The spatial patterns and probability distributions are generally well represented but skill scores that measure the degree to which the frequencies of maximum variance are captured are consistently lower for most ESMs and climate modes. Substantial variability in skill scores manifests across realizations from individual ESMs for the PNA and oceanic modes. Further, the ESMs consistently overestimate the strength of the NAM-PNA first-order interaction and underestimate the NAM-AMO connection. These results suggest that the choice of ESM and ESM realizations will continue to play a critical role in determining climate projections at the global and regional scale at least in the near-term.

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.

scholarly journals Constraints on probability distributions of grammatical forms

Psihologija ◽  
2007 ◽  
Vol 40 (1) ◽  
pp. 5-35
Author(s):  
Aleksandar Kostic ◽  
Milena Bozic
Keyword(s):  
Probability Distribution ◽  
Relative Entropy ◽  
Probability Distributions ◽  
The Third ◽  
Singular Form ◽  
And Gender ◽  
Grammatical Number ◽  
Morphological System

In this study we investigate the constraints on probability distribution of grammatical forms within morphological paradigms of Serbian language, where paradigm is specified as a coherent set of elements with defined criteria for inclusion. Thus, for example, in Serbian all feminine nouns that end with the suffix "a" in their nominative singular form belong to the third declension, the declension being a paradigm. The notion of a paradigm could be extended to other criteria as well, hence, we can think of noun cases, irrespective of grammatical number and gender, or noun gender, irrespective of case and grammatical number, also as paradigms. We took the relative entropy as a measure of homogeneity of probability distribution within paradigms. The analysis was performed on 116 morphological paradigms of typical Serbian and for each paradigm the relative entropy has been calculated. The obtained results indicate that for most paradigms the relative entropy values fall within a range of 0.75 - 0.9. Nonhomogeneous distribution of relative entropy values allows for estimating the relative entropy of the morphological system as a whole. This value is 0.69 and can tentatively be taken as an index of stability of the morphological system.

scholarly journals Posterior Probability on Finite Set

2012 ◽  
Vol 20 (4) ◽  
pp. 257-263
Author(s):  
Hiroyuki Okazaki
Keyword(s):  
Probability Distribution ◽  
Probability Measure ◽  
Posterior Probability ◽  
Probability Distributions ◽  
Sample Space ◽  
Finite Sample ◽  
Finite Set

Summary In [14] we formalized probability and probability distribution on a finite sample space. In this article first we propose a formalization of the class of finite sample spaces whose element’s probability distributions are equivalent with each other. Next, we formalize the probability measure of the class of sample spaces we have formalized above. Finally, we formalize the sampling and posterior probability.

scholarly journals Bayesian estimation of the seroprevalence of antibodies to SARS-CoV-2

JAMIA Open ◽  
2020 ◽  
Author(s):  
Qunfeng Dong ◽  
Xiang Gao
Keyword(s):  
Probability Distribution ◽  
Large Scale ◽  
Prior Probability ◽  
Probability Distributions ◽  
Single Point ◽  
Point Estimates ◽  
Specificity And Sensitivity ◽  
Large Scale Dataset ◽  
The Us ◽  
Antibody Tests

Abstract Accurate estimations of the seroprevalence of antibodies to severe acute respiratory syndrome coronavirus 2 need to properly consider the specificity and sensitivity of the antibody tests. In addition, prior knowledge of the extent of viral infection in a population may also be important for adjusting the estimation of seroprevalence. For this purpose, we have developed a Bayesian approach that can incorporate the variabilities of specificity and sensitivity of the antibody tests, as well as the prior probability distribution of seroprevalence. We have demonstrated the utility of our approach by applying it to a recently published large-scale dataset from the US CDC, with our results providing entire probability distributions of seroprevalence instead of single-point estimates. Our Bayesian code is freely available at https://github.com/qunfengdong/AntibodyTest.

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