Probability distributions in a two-parameter scaling theory of localization

1988 ◽  
Vol 37 (18) ◽  
pp. 10571-10580 ◽  
Author(s):  
J. Heinrichs
Keyword(s):  
Probability Distributions ◽  
Scaling Theory ◽  
Two Parameter

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 10 (4) ◽  
pp. 4597-4626
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Joint Probability ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Wide Variability ◽  
Multiple Variables ◽  
Two Parameter ◽  
Non Parametric

Abstract. The wide variability of hydrological losses in catchments is due to multiple variables that affect the rainfall-runoff process. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall-runoff models. Using representative single values of losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. Probability distributions can be used as a better representation of losses. In particular, using joint probability approaches (JPA), probability distributions can be incorporated into hydrological loss parameters in design models. However, lack of understanding of loss distributions limits the benefit of using JPA. The aim of this paper is to identify a probability distribution function that can successfully describe hydrological losses in South Australian (SA) catchments. This paper describes suitable parametric and non-parametric distributions that can successfully describe observed loss data. The goodness-of-fit of the fitted distributions and quantification of the errors associated with quantile estimation are also discussed a two-parameter Gamma distribution was identified as one that successfully described initial loss (IL) data of the selected catchments. Also, a non-parametric standardised distribution of losses that describes both IL and continuing loss (CL) data were identified. The results obtained for the non-parametric methods were compared with similar studies carried out in other parts of Australia and a remarkable degree of consistency was observed. The results will be helpful in improving design flood applications.

Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter

2021 ◽  
Vol 127 (1) ◽  
pp. 111-130
Author(s):  
Dimitris Askitis
Keyword(s):  
Distribution Function ◽  
Beta Distribution ◽  
Probability Distributions ◽  
Beta Function ◽  
Incomplete Beta Function ◽  
Univariate Function ◽  
Convexity Properties ◽  
Logarithmic Concavity ◽  
Two Parameter ◽  
Monotonicity Results

The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as a univariate function of the first parameter. Monotonicity, limit results and convexity properties are provided. In particular, logarithmic concavity of the inverse incomplete beta function is established. In addition, we provide monotonicity results on inverses of a larger class of parametrised distributions that may be of independent interest.

scholarly journals Effect of water absorption on the Weibull distribution of fatigue test in jute-reinforced polyester composite materials

2019 ◽  
Vol 28 ◽  
pp. 096369351985383 ◽  
Author(s):  
Djamel Djeghader ◽  
Bachir Redjel
Keyword(s):  
Composite Materials ◽  
Weibull Distribution ◽  
Probability Distributions ◽  
Correlation Coefficients ◽  
Statistical Correlation ◽  
Polyester Composite ◽  
Polyester Matrix ◽  
Number Of Cycles ◽  
Cycles To Failure ◽  
Two Parameter

Composite materials have been manufactured using bidirectional jute yarn in a polyester matrix. The manufactured composite has been subjected to water aging for various times of immersion (90, 180, and 270 days). A significant decrease of fatigue strength has been observed during water aging. The number of cycles to failure of the aged and nonaged specimens were correlated using the two-parameter Weibull distribution function to determine the probability of failure and plot the S–N curves at different reliability levels. The results have shown that the two-parameter Weibull distribution describes the fatigue life probability distributions of jute-reinforced polyester composite material with highly significant statistical correlation coefficients.

scholarly journals Two-parameter scaling theory of transport near a spectral node

2014 ◽  
Vol 90 (17) ◽  
Author(s):  
Andreas Sinner ◽  
Klaus Ziegler
Keyword(s):  
Scaling Theory ◽  
Two Parameter

scholarly journals Fracture Statistics Using Three-Parameter and Two-Parameter Weibull Distributions for Fe-0.4C-1.5Cr-1.5Ni-0.8Mn-0.2Mo Structural Sintered Steel

2016 ◽  
Vol 61 (3) ◽  
pp. 1547-1554 ◽  
Author(s):  
Ch. Fiał ◽  
A. Ciaś ◽  
A. Czarski ◽  
M. Sułowski
Keyword(s):  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Sufficient Evidence ◽  
Parameter Distribution ◽  
Sintered Steel ◽  
Weibull Statistics ◽  
Sintered Steels ◽  
Anderson Darling ◽  
Two Parameter

Abstract A statistical analysis is presented of tensile and bending strengths of a porous sintered structural steel which exhibits non-linear, quasi-brittle, behaviour. It is the result of existing natural flaws (pores and oxide inclusions) and of the formation of fresh flaws when stress is applied. The analysis is by two- and three-parameter Weibull statistics. Weibull modulus, a measure of reliability, was estimated by the maximum likelihood method for specimen populations < 30. Probability distributions were compared on the basis of goodness to fit using the Anderson-Darling tests. The use of the two-parameter Weibull distribution for strength data of quasi-brittle sintered steels is questioned, because there is sufficient evidence that the 3-parameter distribution fits the data better.

scholarly journals A Novel Generator of Continuous Probability Distributions for the Asymmetric Left-skewed Bimodal Real-life Data with Properties and Copulas

2021 ◽  
pp. 943-961 ◽  
Author(s):  
Wahid A. M. Shehata ◽  
Haitham Yousof ◽  
Mohamed Aboraya
Keyword(s):  
Probability Distributions ◽  
Real Life ◽  
Real Data ◽  
Moment Generating Function ◽  
Data Sets ◽  
Base Line ◽  
Survival Times ◽  
New Family ◽  
Real Life Data ◽  
Two Parameter

This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived.  Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.

scholarly journals Snowmelt-Related Flood Risk in Appalachia: First Estimates from a Historical Snow Climatology

2006 ◽  
Vol 45 (1) ◽  
pp. 178-193 ◽  
Author(s):  
Daniel Y. Graybeal ◽  
Daniel J. Leathers
Keyword(s):  
Snow Depth ◽  
Probability Distributions ◽  
Gumbel Distribution ◽  
The United States ◽  
Return Periods ◽  
Regional Patterns ◽  
Depth Data ◽  
Maximum Snow Depth ◽  
Two Parameter

Abstract A first attempt has been made toward quantifying the risk of snowmelt-related flooding in the central and southern Appalachian Mountains of the United States (from 35° to 42°N). In the last decade, two major events occurred within the region, prompting this study. Snowfall and snow depth data were collected from the cooperative observer network, quality controlled, and summarized at seasonal resolution (December–March). For establishing regional patterns, the period of 1971–2000 was selected. For testing fits of candidate probability distributions, and for focusing on the sparsely sampled higher elevations, this criterion was relaxed to include as many data from the mid- to late century as were reasonably admissible. Results indicate that the two-parameter Gumbel distribution fit best both the seasonal total snowfall and seasonal maximum snow depth. That distribution was then used to map return periods associated with critical seasonal snowfall and maximum snow depth masses. Seasonal snowfall amounts linked to a role for snowmelt in flooding were found to occur at return periods of from 2–5 yr in Pennsylvania and West Virginia to 10–200 yr in North Carolina. More generally, at elevations of at least 600 m throughout the region, return periods of 10–25 yr were estimated for critical levels of two flood-related criteria: seasonal total snowfall and maximum snow depth. In addition to providing valuable climatological information to aid forecasters and analysts, the results also support the need for further work toward understanding the role of snow in Appalachian floods.

COMPARISON OF WEIBULL AND NORMAL PROBABILITY DISTRIBUTION OF FLEXURAL STRENGTH OF DENSE AND POROUS FIRED CLAY

2016 ◽  
Vol 78 (9) ◽  
Author(s):  
Muazu Abubakar ◽  
Muhamad Azizi Mat Yajid ◽  
Norhayati Ahmad
Keyword(s):  
Probability Distribution ◽  
Flexural Strength ◽  
Normal Distribution ◽  
Probability Distributions ◽  
Bending Test ◽  
Strength Data ◽  
Normal Probability ◽  
Distribution Parameters ◽  
Normal Probability Distribution ◽  
Two Parameter

In this research, dense and porous fired clay were produced at a firing temperature of 1300°C. The flexural strength data of the dense and the porous fired clay were determined using three point bending test. Two-parameter Weibull and normal probability distributions were used to estimate the reliability of the flexural strength data of the dense and the porous fired clay. From the result, the Weibull probability distribution scale parameter for the dense (36.31MPa) and Porous (18.85MPa) fired clay are higher than the mean strength value for the dense (33.84MPa) and the porous (17.87MPa) of the normal distribution. Distributions of flaws in the dense and the porous fired clay have a significant effect on the Weibull and normal distribution parameters. The fractured surface of the dense fired clay shows a random distribution of cracks while that of the porous fired clay shows a distribution of pores in the morphology. The normal distribution considers failure at 50% of the flexural strength data while Weibull probability distribution is failure at 62.3% of the strength data. Therefore, two-parameter Weibull is the suitable tool to model failure strength data of the dense and porous fired clay.  

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