probability distribution
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2022 ◽  
Vol 95 ◽  
pp. 102180
Author(s):  
Chao-Huang Cai ◽  
Yan-Gang Zhao ◽  
Zhao-Hui Lu ◽  
Yu Leng

2022 ◽  
Vol 103 ◽  
pp. 103175
Author(s):  
Feng Li ◽  
Wangxing Xue ◽  
Ying Rong ◽  
Canyi Du ◽  
Jilong Tang ◽  
...  

Author(s):  
Eddy Keming Chen ◽  
Roderich Tumulka

AbstractLet $$\mathscr {H}$$ H be a finite-dimensional complex Hilbert space and $$\mathscr {D}$$ D the set of density matrices on $$\mathscr {H}$$ H , i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on $$\mathscr {D}$$ D that can be regarded as the uniform distribution over $$\mathscr {D}$$ D . We propose a measure on $$\mathscr {D}$$ D , argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to this measure.


MAUSAM ◽  
2022 ◽  
Vol 73 (1) ◽  
pp. 139-150
Author(s):  
VIKRAM KUMAR ◽  
SHAKTI BALA ◽  
BHAR TESH

Planning of water resources and its management with the ambiguity and non-uniformity accompanying with precipitation and other meteorological physical characteristics may perhaps effect on agricultural production in Bihar where the farmers mostly depend on precipitation. The precipitation and potential evapotranspiration temporal distribution of the state is irregular due to geomorphology, climatic and other anthropogenic factors of the state. In the present study, attempt is taken to expose the best-fit probability distribution among the various available probability distribution of annual average precipitation and potential evapotranspiration based on 102 year of past records of all 37 districts of the state. On the basis of ranks of goodness of fit tests such as Kolmogorov Smirnov, Anderson Darling and Chi-Squared, the normal distribution was observed the best-fit probability distribution for 11 districts followed by Weibull (3P) for 9 districts, the Beta distribution for 5 districts and other distribution for rest districts for precipitation. Whereas Cauchy distribution was come out with the best-fit probability distribution for potential evapotranspiration for all districts and the second best was Gamma (3P) covering almost 60% of the total districts followed by General Extreme Value distribution (32%). The results can be used in future hydraulic design, hydrological study for estimation of return period and water resource planners for policy development.  


2022 ◽  
Author(s):  
Bradford D. Loucas ◽  
Igor Shuryak ◽  
Stephen R. Kunkel ◽  
Michael N. Cornforth

The relationship between certain chromosomal aberration (CA) types and cell lethality is well established. On that basis we used multi-fluor in situ hybridization (mFISH) to tally the number of mitotic human lymphocytes exposed to graded doses of gamma rays that carried either lethal or nonlethal CA types. Despite the fact that a number of nonlethal complex exchanges were observed, the cells containing them were seldom deemed viable, due to coincident lethal chromosome damage. We considered two model variants for describing the dose responses. The first assumes independent linear-quadratic (LQ) dose response shapes for the yields of both lethal and nonlethal CAs. The second (simplified) variant assumes that the mean number of nonlethal CAs per cell is proportional to the mean number of lethal CAs per cell, meaning that the shapes and magnitudes of both aberration types differ only by a multiplicative proportionality constant. Using these models allowed us to assemble dose response curves for the frequency of aberration-bearing cells that would be expected to survive. This took the form of a joint probability distribution for cells containing ≥1 nonlethal CAs but having zero lethal CAs. The simplified second model variant turned out to be marginally better supported than the first, and the joint probability distribution based on this model yielded a crescent-shaped dose response reminiscent of those observed for mutagenesis and transformation for cells “at risk” (i.e. not corrected for survival). Among the implications of these findings is the suggestion that similarly shaped curves form the basis for deriving metrics associated with radiation risk models.


Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 125
Author(s):  
Damián G. Hernández ◽  
Inés Samengo

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.


Econometrics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 5
Author(s):  
Ron Mittelhammer ◽  
George Judge ◽  
Miguel Henry

In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing methodology relies on the characteristic function of the population probability distribution being tested and is attractive in that, regardless of the null hypothesis being tested, it provides a unified framework for conducting such tests. The testing procedure is also computationally tractable and relatively straightforward to implement. In contrast to some alternative test statistics, the proposed entropy test is free from user-specified kernel and bandwidth choices, idiosyncratic and complex regularity conditions, and/or choices of evaluation grids. Several simulation exercises were performed to document the empirical performance of our proposed test, including a regression example that is illustrative of how, in some contexts, the approach can be applied to composite hypothesis-testing situations via data transformations. Overall, the testing procedure exhibits notable promise, exhibiting appreciable increasing power as sample size increases for a number of alternative distributions when contrasted with hypothesized null distributions. Possible general extensions of the approach to composite hypothesis-testing contexts, and directions for future work are also discussed.


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