Properties of the three-parameter log normal probability distribution

1975 ◽  
Vol 11 (2) ◽  
pp. 229-235 ◽  
Author(s):  
Stephen J. Burges ◽  
Dennis P. Lettenmaier ◽  
Courtney L. Bates
Keyword(s):  
Probability Distribution ◽  
Normal Probability ◽  
Normal Probability Distribution ◽  
Log Normal

Probabilistic Carbonation Simulations in Concrete Based on Marble Powder

2020 ◽  
Vol 1013 ◽  
pp. 114-119
Author(s):  
Azhar Badaoui
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Random Variable ◽  
Carbonation Depth ◽  
Concrete Carbonation ◽  
Normal Probability ◽  
Powder Diameter ◽  
Marble Powder ◽  
Normal Probability Distribution ◽  
Log Normal

The aim of this paper is the evaluation of concrete carbonation depth from a probabilistic analysis, focusing specifically on the study of the marble powder diameters randomness effect on the reinforced concrete carbonation. Monte Carlo simulations are realized under the assumption that the marble powder diameter (Dmp) is random variable with a log-normal probability distribution.

scholarly journals Performance evaluation and coefficients of reliability for waste stabilization ponds in northeast Brazil

2021 ◽  
Vol 16 (1) ◽  
pp. 1
Author(s):  
Matheus Sales Alves ◽  
Fernando José Araújo da Silva ◽  
André Luís Calado Araújo ◽  
Erlon Lopes Pereira
Keyword(s):  
Northeast Brazil ◽  
Concentration Data ◽  
Waste Stabilization Ponds ◽  
Stabilization Ponds ◽  
Waste Stabilization ◽  
Normal Probability ◽  
Thermotolerant Coliforms ◽  
Normal Probability Distribution ◽  
Log Normal ◽  
Domestic Effluent

This paper assesses the reliability of Waste Stabilization Ponds (WSP) and proposes an alternative approach to WSP design based on the calculation of coefficient of reliability (COR) from an acceptable measure of violation of discharge standards. For that, data were collected from 10 full-scale systems operating in Northeast Brazil. All systems receive predominantly domestic effluent and are composed of one facultative pond and two serial maturation ponds. Different levels of restriction for effluent discharge were considered regarding the parameters: BOD, COD, total suspended solids, ammonia and thermotolerant coliforms. The Log-normal Probability Distribution Function (PDF) was able to represent the behavior of the concentration data in the effluent and, therefore, allowed the COR calculation. The COR was obtained from the coefficient of variation (CV) of the concentrations and the standardized normal variable associated with a 95% probability of non-exceedance. The observed dispersion of the results proved to be detrimental to the adoption of a single COR value for the evaluated parameters. In addition, the comparison between observed and design/operational concentration for optimal performance showed that the 95% reliability scenario represents a less achievable target for WSP systems.

Linear model analysis of net catch data using the negative binomial distribution

1999 ◽  
Vol 56 (2) ◽  
pp. 191-200 ◽  
Author(s):  
James H Power ◽  
E Barry Moser
Keyword(s):  
Probability Distribution ◽  
Linear Model ◽  
Negative Binomial ◽  
Aquatic Organisms ◽  
Mean Value ◽  
Model Parameters ◽  
Catch Data ◽  
Normal Probability ◽  
Estimation Of Model Parameters ◽  
Normal Probability Distribution

Sampling with nets or trawls remains a common technique for determining the comparative abundances of aquatic organisms, and the objective of such studies is frequently to evaluate relationships among the counts of individuals caught and exogenous variables. Analysis of such data is often done with a general linear model (e.g., ANOVA, ANCOVA, regression), assuming an underlying normal probability distribution. Such analyses are not fully satisfactory because of the symmetry and continuous nature of the assumed normal probability distribution and the high variance to low mean value relationships common to counts of biological populations. The negative binomial is a discrete probability distribution that is recognized as a suitable descriptor of organism count data. We present an approach for undertaking linear model analyses of net catch data that permits estimation of model parameters (including the negative binomial k parameter) and hypothesis testing of both continuous and discrete model effects and their interactions using bootstrap replication. The analysis incorporates adjustment for varying element sizes, such as differences in the amounts of water filtered during sampling.

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