Probability Distributions (Normal and Log-Normal)

2018 ◽  
pp. 257-264
Keyword(s):  
Probability Distributions ◽  
Log Normal

scholarly journals Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

Reliability Against Drifting Ice—An Adjunct to Monte Carlo Simulation

1991 ◽  
Vol 113 (3) ◽  
pp. 253-259
Author(s):  
A. B. Dunwoody
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Normal Family ◽  
Probability Distributions ◽  
Load Model ◽  
Ice Load ◽  
Ice Loads ◽  
Drifting Ice ◽  
Log Normal ◽  
Monte Carlo Simulation Program

A method is presented for the calculation of the reliability of a structure against drifting ice subject to restrictions on the form of the ice load model and on the form of the probability distributions of the ice feature characteristics. The ice load model must have the form that the ice load is proportional to the product of the characteristics of the impacting ice feature raised to individual powers. Results from a Monte Carlo simulation program are presented to demonstrate that the ice loads for a number of useful ice interaction scenarios can be modeled by an equation of this form. The probability distributions of the ice feature characteristics must be from the log-normal family. A realistic example using publicly available ice data and ice load model is presented.

scholarly journals The Nested_fit Data Analysis Program

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 14 ◽  
Author(s):  
Martino Trassinelli
Keyword(s):  
Data Analysis ◽  
Probability Distributions ◽  
Analysis Program ◽  
Large Database ◽  
Data Set ◽  
Lawn Mower ◽  
Bayesian Data Analysis ◽  
Bayesian Evidence ◽  
Spectral Profiles ◽  
Log Normal

We present here Nested_fit, a Bayesian data analysis code developed for investigations of atomic spectra and other physical data. It is based on the nested sampling algorithm with the implementation of an upgraded lawn mower robot method for finding new live points. For a given data set and a chosen model, the program provides the Bayesian evidence, for the comparison of different hypotheses/models, and the different parameter probability distributions. A large database of spectral profiles is already available (Gaussian, Lorentz, Voigt, Log-normal, etc.) and additional ones can easily added. It is written in Fortran, for an optimized parallel computation, and it is accompanied by a Python library for the results visualization.

Stieltjes classes for moment-indeterminate probability distributions

2004 ◽  
Vol 41 (A) ◽  
pp. 281-294 ◽  
Author(s):  
Jordan Stoyanov
Keyword(s):  
Probability Distributions ◽  
Classical Problem ◽  
Inverse Gaussian ◽  
Positive Order ◽  
Power Transformations ◽  
Log Normal ◽  
Open Question ◽  
Indeterminate Probability ◽  
Index Of Dissimilarity ◽  
Finite Moments

Let F be a probability distribution function with density f. We assume that (a) F has finite moments of any integer positive order and (b) the classical problem of moments for F has a nonunique solution (F is M-indeterminate). Our goal is to describe a , where h is a ‘small' perturbation function. Such a class S consists of different distributions Fε (fε is the density of Fε) all sharing the same moments as those of F, thus illustrating the nonuniqueness of F, and of any Fε, in terms of the moments. Power transformations of distributions such as the normal, log-normal and exponential are considered and for them Stieltjes classes written explicitly. We define a characteristic of S called an index of dissimilarity and calculate its value in some cases. A new Stieltjes class involving a power of the normal distribution is presented. An open question about the inverse Gaussian distribution is formulated. Related topics are briefly discussed.

scholarly journals M-dwarf exoplanet surface density distribution

2018 ◽  
Vol 612 ◽  
pp. L3 ◽  
Author(s):  
Michael R. Meyer ◽  
Adam Amara ◽  
Maddalena Reggiani ◽  
Sascha P. Quanz
Keyword(s):  
Density Distribution ◽  
Surface Density ◽  
Probability Distributions ◽  
Mass Range ◽  
Normal Function ◽  
Point Estimates ◽  
Points Of View ◽  
Log Normal ◽  
Parameter Values ◽  
M Dwarf

Aims. We fit a log-normal function to the M-dwarf orbital surface density distribution of gas giant planets, over the mass range 1–10 times that of Jupiter, from 0.07 to 400 AU. Methods. We used a Markov chain Monte Carlo approach to explore the likelihoods of various parameter values consistent with point estimates of the data given our assumed functional form. Results. This fit is consistent with radial velocity, microlensing, and direct-imaging observations, is well-motivated from theoretical and phenomenological points of view, and predicts results of future surveys. We present probability distributions for each parameter and a maximum likelihood estimate solution. Conclusions. We suggest that this function makes more physical sense than other widely used functions, and we explore the implications of our results on the design of future exoplanet surveys.

Textural properties of regoliths on vegetated steep slopes in upland regions, Scotland

1986 ◽  
Vol 77 (3) ◽  
pp. 241-250 ◽  
Author(s):  
J. L. Innes
Keyword(s):  
Particle Size ◽  
Early Stage ◽  
Probability Distributions ◽  
Textural Properties ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Normal Probability ◽  
Log Normal ◽  
Steep Slopes

ABSTRACTThe textural properties of many sediments provide a good indication of their provenance, but surprisingly little information is available on the transitional stages between the breakdown of a rock and the incorporation of the material into a fluvial sediment. These transitional stages are important as certain fractions (particularly the finer ones) may be selectively removed. Regoliths developed on steep slopes represent an early stage in the debris cascade and they are here examined in detail to assess the role of parent lithology on the textural properties of the regolith. There are substantial variations between lithologies, although the majority of regoliths are dominated by coarser fractions and are poorly sorted. Most particle size distributions show some degree of fit to both log-normal probability distributions and Rosin distributions. Differences from these can be ascribed to the processes operating on steep slopes, particularly the influx of sand- and silt-sized material by colluvial processes and the removal of clay-sized material by leaching. The regoliths form a distinct facies type which may be recognisable in the geological record.

scholarly journals Strategic formulation of industrial maintenance based on equipment reliability in a sugar and ethanol production plant

2020 ◽  
Vol 11 (7) ◽  
pp. 2592-2612
Author(s):  
Elias Tadeu da Silva ◽  
Jorge alberto Achcar ◽  
Claudio Luis Piratelli
Keyword(s):  
Probability Distributions ◽  
Production Plant ◽  
Competitive Advantages ◽  
Maintenance Strategy ◽  
Equipment Reliability ◽  
Reliability Centered Maintenance ◽  
Equipment Failures ◽  
The Times ◽  
Definition Of ◽  
Log Normal

Maintenance and management have substantial importance in the search of the company’s competitive advantages. In this direction, a reliability analysis of  equipments is very important for the definition of the most suitable maintenance strategy. The main goal of this paper is to assess the reliability-centered maintenance of the industrial reliability curve of a sugar cane department of an industry located in São Paulo State, Brazil. The proposed research method was based on the application of existing statistical modeling for the times between failures (TBF) of all reported equipment failures or the interruption times in the production line. These times were modeled by standard lifetime probability distributions as log-normal and Weibull distributions. The results showed that the company's strategy for preventive maintenance during the off-season is not adequate and the statistical analysis also identified important factors that affect the company's maintenance strategy. These results could be of great interest for the company and for engineering applications in general.

Standard distributions in R.

2021 ◽  
pp. 335-347
Author(s):  
Donald L. J. Quicke ◽  
Buntika A. Butcher ◽  
Rachel A. Kruft Welton
Keyword(s):  
Programming Language ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Test Statistics ◽  
P Values ◽  
Chi Squared ◽  
Student’S T ◽  
Log Normal

Abstract There are a number of in-built probability distributions, including uniform, binomial, negative binomial, normal, log-normal, logistic, exponential, Chisquared, Poisson, gamma, Fisher's F, Student's t, Weibull and others. These are used to generate p-values from test statistics, to generate random values from a distribution or to generate expected distributions. This chapter deals with standard distributions in R (a programming language that has a huge range of inbuilt statistical and graphical functions), focusing on the normal, Student's t, lognormal, logistic, Poisson, gamma, and the Chi-squared.

Statistical Analysis of Langmuir Waves Associated with Type III Radio Bursts: I. Wind Observations

2011 ◽  
Vol 20 (4) ◽  
Author(s):  
S. Vidojević ◽  
A. Zaslavsky ◽  
M. Maksimović ◽  
M. Dražić ◽  
O. Atanacković
Keyword(s):  
Plasma Frequency ◽  
Probability Distributions ◽  
Langmuir Waves ◽  
Type Iii ◽  
Power Spectral ◽  
Spectrum Density ◽  
Wind Spacecraft ◽  
Log Normal ◽  
The Waves ◽  
Log Normal Distribution

AbstractInterplanetary electron beams are unstable in the solar wind and they generate Langmuir waves at the local plasma frequency or its harmonic. Radio observations of the waves in the range 4-256 kHz, observed in 1994-2010 with the WAVES experiment onboard the WIND spacecraft, are statistically analyzed. A subset of 36 events with Langmuir waves and type III bursts occurring at the same time was selected. After removal of the background, the remaining power spectral density is modeled by the Pearson system of probability distributions (types I, IV and VI). The Stochastic Growth Theory (SGT) predicts log-normal distribution for the power spectrum density of the Langmuir waves. Our results indicate that SGT possibly requires further verification.

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