scholarly journals The Probability Distribution of Worldwide Forest Areas

2021 ◽  
Vol 13 (3) ◽  
pp. 1361
Author(s):  
Rafael González-Val
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Power Law ◽  
Power Laws ◽  
Theoretical Models ◽  
Forest Growth ◽  
Plausible Model ◽  
Forest Coverage ◽  
Log Normal ◽  
Log Normal Distribution

This paper analyses the probability distribution of worldwide forest areas. We find moderate support for a Pareto-type distribution (power law) using FAO data from 1990 to 2015. Power laws are common features of many complex systems in nature. A power law is a plausible model for the world probability distribution of forest areas in all examined years, although the log-normal distribution is a plausible alternative model that cannot be rejected. The random growth of forest areas could generate a power law or log-normal distribution. We study the change in forest coverage using parametric and non-parametric methods. We identified a slight convergence of forest areas over the time reviewed; however, random forest area growth cannot be rejected for most of the distribution of forest areas. Therefore, our results give support to theoretical models of stochastic forest growth.

FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS

2006 ◽  
Vol 17 (10) ◽  
pp. 1429-1436 ◽  
Author(s):  
LUCIEN BENGUIGUI ◽  
EFRAT BLUMENFELD-LIEBERTHAL
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Lognormal Distribution ◽  
Size Distributions ◽  
New Classification ◽  
Multiplicative Process ◽  
Random Multiplicative Process ◽  
Log Normal ◽  
Log Normal Distribution

We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.

scholarly journals Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 908
Author(s):  
Atushi Ishikawa ◽  
Shouji Fujimoto ◽  
Arturo Ramos ◽  
Takayuki Mizuno
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Time Variation ◽  
Time Reversal ◽  
Urban Population ◽  
Large Scale ◽  
Time Reversal Symmetry ◽  
Scale Range ◽  
Log Normal ◽  
Log Normal Distribution

We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry.

scholarly journals Estimation on Reliability Models of Bearing Failure Data

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Xia Xintao ◽  
Chang Zhen ◽  
Zhang Lijun ◽  
Yang Xiaowei
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Normal Distribution ◽  
Distribution Model ◽  
Bearing Failure ◽  
Analysis Model ◽  
Failure Data ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Two Parameter

The failure data of bearing products is random and discrete and shows evident uncertainty. Is it accurate and reliable to use Weibull distribution to represent the failure model of product? The Weibull distribution, log-normal distribution, and an improved maximum entropy probability distribution were compared and analyzed to find an optimum and precise reliability analysis model. By utilizing computer simulation technology and k-s hypothesis testing, the feasibility of three models was verified, and the reliability of different models obtained via practical bearing failure data was compared and analyzed. The research indicates that the reliability model of two-parameter Weibull distribution does not apply to all situations, and sometimes, two-parameter log-normal distribution model is more precise and feasible; compared to three-parameter log-normal distribution model, the three-parameter Weibull distribution manifests better accuracy but still does not apply to all cases, while the novel proposed model of improved maximum entropy probability distribution fits not only all kinds of known distributions but also poor information issues with unknown probability distribution, prior information, or trends, so it is an ideal reliability analysis model with least error at present.

scholarly journals Distribution of Earthquake Magnitude Levels in Bangladesh

2019 ◽  
Vol 11 (3) ◽  
pp. 15
Author(s):  
Md. Habibur Rahman ◽  
Md. Moyazzem Hossain
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Earthquake Magnitude ◽  
Human Beings ◽  
Richter Scale ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Best Fit

Earthquakes are one of the main natural hazards which seriously make threats the life and property of human beings. Different probability distributions of the earthquake magnitude levels in Bangladesh are fitted. In terms of graphical assessment and goodness-of-fit criterion, the log-normal distribution is found to be the best fit probability distributions for the earthquake magnitude levels in Bangladesh among the probability distribution considered in this study. The average earthquake magnitude level found 4.67 (in Richter scale) for log-normal distribution and the approximately forty-six percent chance is predicted to take place earthquake magnitude in the interval four to five.

scholarly journals The latitude dependence and probability distribution of polar mesospheric turbulence

2006 ◽  
Vol 6 (6) ◽  
pp. 12199-12216 ◽  
Author(s):  
M. Rapp ◽  
E. Becker ◽  
B. Strelnikov ◽  
F.-J. Lübken
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Circulation Model ◽  
Global Circulation Model ◽  
Latitude Dependence ◽  
Dissipation Rates ◽  
Latitudinal Dependence ◽  
Resolution Model ◽  
Log Normal ◽  
Log Normal Distribution

Abstract. We consider in-situ observations and results from a global circulation model to study the latitude dependence and probability distribution of polar mesospheric turbulence. A comparison of summer observations at 69° N and 79° N shows that mesospheric turbulence weakens towards the summer pole. Furthermore, these data suggest that at both latitudes in about ~70% of all samples there are non-turbulent altitude bins in the considered altitude range between 70 and 95 km. The remaining 30% with detectable turbulence show an approximately log-normal distribution of dissipation rates. A low-resolution model version with a gravity wave (GW) parameterization explains the observed latitude dependence as a consequence of a downshift of the breaking levels towards the summer pole and an accompanying decay of turbulent heating per unit mass. When we do not use a GW parameterization but employ a high spatial resolution instead to simulate GW effects explicitly, the model predicts a similar latitudinal dependence with weakening turbulence towards the summer pole. In addition, the model also produces a log-normal distribution of dissipation rates. The simulated probability distribution is more narrow than in the observations since the model resolves at most mid-frequency GWs, whereas real turbulence is also excited by smaller-scale disturbances. The GW resolving simulation suggests a weaker tropospheric GW source at polar latitudes as the dominating mechanism for the latitudinal dependence.

scholarly journals Using a combined power law and log-normal distribution model to simulate particle formation and growth in a mobile aerosol chamber

2016 ◽  
Author(s):  
M. Olin ◽  
T. Anttila ◽  
M. Dal Maso
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Particle Formation ◽  
Distribution Model ◽  
Aerosol Formation ◽  
Aerosol Chamber ◽  
Relative Errors ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Particle Formation And Growth

Abstract. We present the combined power law and log-normal distribution (PL+LN) model, a computationally efficient model to be used in simulations where the particle size distribution cannot be accurately represented by log-normal distributions, such as in simulations involving the initial steps of aerosol formation, where new particle formation and growth occur simultaneously, or in the case of inverse modelling. The model was validated against highly accurate sectional models using input parameter values that reflect conditions typical to particle formation occurring in the atmosphere and in vehicle exhaust, and tested in the simulation of a particle formation event performed in a mobile aerosol chamber at Mäkelänkatu street canyon measurement site in Helsinki, Finland. The number, surface area, and mass concentrations in the chamber simulation were conserved with the relative errors lower than 2 % using the PL+LN model, whereas a moment-based log-normal model and sectional models with the same computing time as with the PL+LN model caused relative errors up to 10 % and 135 %, respectively.

scholarly journals Theoretical Models for the Quantification of Lung Injury Using Ventilation and Perfusion Distributions

2009 ◽  
Vol 10 (2) ◽  
pp. 139-154 ◽  
Author(s):  
B. S. Brook ◽  
C. M. Murphy ◽  
D. Breen ◽  
A. W. Miles ◽  
D. G. Tilley ◽  
...  
Keyword(s):  
Statistical Model ◽  
Lung Disease ◽  
Normal Distribution ◽  
Theoretical Models ◽  
Tree Model ◽  
Flow Through ◽  
Left And Right ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Ventilation And Perfusion

This paper describes two approaches to modelling lung disease: one based on a multi-compartment statistical model with a log normal distribution of ventilation perfusion ratio (V˙/Q˙) values; and the other on a bifurcating tree which emulates the anatomical structure of the lung. In the statistical model, the distribution becomes bimodal, when theV˙/Q˙values of a randomly selected number of compartments are reduced by 85% to simulate lung disease. For the bifurcating tree model a difference in flow to the left and right branches coupled with a small random variation in flow ratio between generations results in a log normal distribution of flows in the terminal branches. Restricting flow through branches within the tree to simulate lung disease transforms this log normal distribution to a bi-modal one. These results are compatible with those obtained from experiments using the multiple inert gas elimination technique, where log normal distributions ofV˙/Q˙ratio become bimodal in the presence of lung disease.

scholarly journals Using a combined power law and log-normal distribution model to simulate particle formation and growth in a mobile aerosol chamber

2016 ◽  
Vol 16 (11) ◽  
pp. 7067-7090 ◽  
Author(s):  
Miska Olin ◽  
Tatu Anttila ◽  
Miikka Dal Maso
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Particle Formation ◽  
Distribution Model ◽  
Aerosol Formation ◽  
Aerosol Chamber ◽  
Relative Errors ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Particle Formation And Growth

Abstract. We present the combined power law and log-normal distribution (PL+LN) model, a computationally efficient model to be used in simulations where the particle size distribution cannot be accurately represented by log-normal distributions, such as in simulations involving the initial steps of aerosol formation, where new particle formation and growth occur simultaneously, or in the case of inverse modeling. The model was evaluated against highly accurate sectional models using input parameter values that reflect conditions typical to particle formation occurring in the atmosphere and in vehicle exhaust. The model was tested in the simulation of a particle formation event performed in a mobile aerosol chamber at Mäkelänkatu street canyon measurement site in Helsinki, Finland. The number, surface area, and mass concentrations in the chamber simulation were conserved with the relative errors lower than 2 % using the PL+LN model, whereas a moment-based log-normal model and sectional models with the same computing time as with the PL+LN model caused relative errors up to 17 and 79 %, respectively.

A Large Scale Fatigue Test of Aluminium Specimens

1965 ◽  
Vol 16 (4) ◽  
pp. 307-322 ◽  
Author(s):  
N. T. Bloomer ◽  
T. F. Roylance
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Normal Distribution ◽  
Probability Of Failure ◽  
Distribution Functions ◽  
Experimental Results ◽  
Normal Distribution Function ◽  
The Mean ◽  
Log Normal ◽  
Log Normal Distribution

SummaryThere have been, in the past, many fatigue tests carried out on a variety of materials and components. These all indicate a wide scattering in the lives (measured by the number of stress cycles to failure) endured by nominally identical components subjected to nominally identical forces before failure occurs. To interpet this scattering several equations have been suggested as representing the statistical distribution functions that fit the lives obtained for individual types of component. Of these functions the log normal distribution function has been perhaps the most widely used. For the central regions of the probability distribution, i.e. about the mean, the log normal distribution and several others represent experimental results very closely indeed, but engineers and designers of all kinds dare not design on the mean fatigue life. They are concerned with specifications that either exclude the possibility of failure or admit only a very small probability of failure. It is thus with the accuracy with which the “lower tail” of the probability distribution curve fits the experimental results that they are concerned.To assess the fit at this lower end for one type of component, a large number (about 1,000) of aluminium specimens have been tested and the corresponding lives plotted. The results are very interesting. They show clearly that the log normal distribution for this type of component and material is pessimistic for a probability of failure of less than 0·3. This result is felt by the authors to be of very great importance. It has further been shown that the use of the “one-sided censored distribution function”, used previously by one of the authors, gives a curve that will fit the lower results better than the complete log normal distribution would do.It is with the testing procedure adopted, the specimens used, the distribution functions considered and the conclusions obtained therefrom that this paper is concerned.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

Sign in / Sign up

Export Citation Format

Share Document