scholarly journals Using the stretched exponential distribution to model runs of extremes in a daily meteorological variable

2015 ◽  
Vol 65 (2) ◽  
pp. 233-246
Author(s):  
W Grace
Keyword(s):  
Exponential Distribution ◽  
Meteorological Variable ◽  
Stretched Exponential ◽  
Stretched Exponential Distribution

scholarly journals An Investigation of Stretched Exponential Function in Quantifying Long-Term Memory of Extreme Events Based on Artificial Data following Lévy Stable Distribution

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
HongGuang Sun ◽  
Lin Yuan ◽  
Yong Zhang ◽  
Nicholas Privitera
Keyword(s):  
Exponential Distribution ◽  
Exponential Function ◽  
Extreme Events ◽  
Stable Distribution ◽  
Wide Spectrum ◽  
Long Term Memory ◽  
Term Memory ◽  
Stretched Exponential ◽  
Stretched Exponential Distribution

Extreme events, which are usually characterized by generalized extreme value (GEV) models, can exhibit long-term memory, whose impact needs to be quantified. It was known that extreme recurrence intervals can better characterize the significant influence of long-term memory than using the GEV model. Our statistical analyses based on time series datasets following the Lévy stable distribution confirm that the stretched exponential distribution can describe a wide spectrum of memory behavior transition from exponentially distributed intervals (without memory) to power-law distributed ones (with strong memory or fractal scaling property), extending the previous evaluation of the stretched exponential function using Gaussian/exponential distributed random data. Further deviation and discussion of a historical paradox (i.e., the residual waiting time tends to increase with an increasing elapsed time under long-term memory) are also provided, based on the theoretical analysis of the Bayesian law and the stretched exponential distribution.

scholarly journals Epigenetic adaptation prolongs photoreceptor survival during retinal degeneration

2019 ◽  
Author(s):  
Rachayata Dharmat ◽  
Sangbae Kim ◽  
Hehe Liu ◽  
Shangyi Fu ◽  
Yumei Li ◽  
...  
Keyword(s):  
Single Cell ◽  
Exponential Distribution ◽  
Time Course ◽  
Chromatin State ◽  
Retinal Cell ◽  
Marker Genes ◽  
Specific Marker ◽  
Stretched Exponential ◽  
Rod Cells ◽  
Stretched Exponential Distribution

AbstractNeural degenerative diseases often display a progressive loss of cells as a stretched exponential distribution. The mechanisms underlying the survival of a subset of genetically identical cells in a population beyond what is expected by chance alone remains unknown. To gain mechanistic insights underlying prolonged cellular survival, we used Spata7 mutant mice as a model and performed single-cell transcriptomic profiling of retinal tissue along the time course of photoreceptor degeneration. Intriguingly, rod cells that survive beyond the initial rapid cell apoptosis phase progressively acquire a distinct transcriptome profile. In these rod cells, expression of photoreceptor-specific phototransduction pathway genes is downregulated while expression of other retinal cell type-specific marker genes is upregulated. These transcriptomic changes are achieved by modulation of the epigenome and changes of the chromatin state at these loci, as indicated by immunofluorescence staining and single-cell ATAC-seq. Consistent with this model, when induction of the repressive epigenetic state is blocked by in vivo histone deacetylase inhibition, all photoreceptors in the mutant retina undergo rapid degeneration, strongly curtailing the stretched exponential distribution. Our study reveals an intrinsic mechanism by which neural cells progressively adapt to genetic stress to achieve prolonged survival through epigenomic regulation and chromatin state modulation.

scholarly journals MAXIMIZABLE INFORMATIONAL ENTROPY AS A MEASURE OF PROBABILISTIC UNCERTAINTY

2010 ◽  
Vol 24 (17) ◽  
pp. 3461-3468 ◽  
Author(s):  
CONGJIE OU ◽  
AZIZ EL KAABOUCHI ◽  
LAURENT NIVANEN ◽  
JINCAN CHEN ◽  
FRANOIS TSOBNANG ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Virtual Work ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Analytical Investigation ◽  
Informational Entropy ◽  
Virtual Work Principle ◽  
Probabilistic Uncertainty ◽  
Stretched Exponential Distribution ◽  
Measure Of Uncertainty

In this work, we consider a recently proposed entropy S defined by a variational relationship [Formula: see text] as a measure of uncertainty of random variable x. The entropy defined in this way underlies an extension of virtual work principle [Formula: see text] leading to the maximum entropy [Formula: see text]. This paper presents an analytical investigation of this maximizable entropy for several distributions such as the stretched exponential distribution, κ-exponential distribution, and Cauchy distribution.

THE EVIDENCE FOR SELF-ORGANIZED CRITICALITY IN SANDPILE DYNAMICS

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 431-443 ◽  
Author(s):  
J. FEDER
Keyword(s):  
Characteristic Size ◽  
Size Distributions ◽  
Exponential Distributions ◽  
Avalanche Size ◽  
Stretched Exponential ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Stretched Exponential Distribution ◽  
Rotating Drums ◽  
Low Rate

Self-organized criticality (SOC) is thought to describe avalanche dynamics in sandpiles. Experiments on the dynamics of “sandpiles” fall in two broad categories. Sandpiles in rotating drums exhibit periodic large avalanches, which is inconsistent with SOC. Other experiments study sandpiles on a circular support driven by the addition of grains of sand at a low rate from above and centered with respect to the support. The mass of avalanches that drop sand off the support is typically measured by a balance. It has been claimed that the observed avalanche statistics is consistent with SOC. However, I find that experiments described in the literature all have avalanche-size distributions that can be very well described by stretched-exponential distributions. Since the stretched-exponential distribution has a characteristic size, I conclude that the experiments described in the literature are inconsistent with SOC.

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

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