scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

scholarly journals Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria

2020 ◽  
Vol 27 (2) ◽  
pp. 8-15
Author(s):  
J.A. Oyewole ◽  
F.O. Aweda ◽  
D. Oni
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Accurate Estimation ◽  
Weibull Parameters ◽  
Factor Method ◽  
Deviation Method

There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interest. Here, wind data from year 2000 to 2010 for four different locations (Port Harcourt, Ikeja, Kano and Jos) were analysed and the Weibull parameters was determined. The three methods employed are Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM) for estimating Weibull parameters. The method that gave the most accurate estimation of the wind speed was MSDM method, while Energy Pattern Factor Method (EPFM) is the most reliable and consistent method for estimating probability density function of wind. Keywords: Weibull Distribution, Method of Moment, Mean Standard Deviation Method, Energy Pattern Method

scholarly journals THE ENERGY SPECTRA OF SURF WAVES ON A CORAL REEF

1978 ◽  
Vol 1 (16) ◽  
pp. 33 ◽  
Author(s):  
Theodore T. Lee ◽  
Kerry P. Black
Keyword(s):  
Time Series ◽  
Coral Reef ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Shallow Water ◽  
Probability Density ◽  
Density Function ◽  
Linear Wave ◽  
Gain Function ◽  
Fourier Spectra

The transformation of waves crossing a coral reef in Hawaii including the probability density function of the wave heights and periods and the shape of the spectrum is discussed. The energy attenuation and the change of height and period statistics is examined using spectral analysis and the zero up-crossing procedure. Measurements of waves at seven points along a 1650 ft transect in depths from 1 to 3.5 ft on the reef and 35 ft offshore were made. The heights were tested for Rayleigh, truncated Rayleigh and Wei bull distributions. A symmetrical distribution presented by Longuet-Higgins (1975) and the Weibull distribution were compared to the wave period density function. In both cases the Weibull probability density function fitted with a high degree of correlation. Simple procedures to obtain Weibull coefficients are given. Fourier spectra were generated and contours of cumulative energy against each position on the reef show the shifting of energy from the peak as the waves move into shallow water. A design spectrum, with the shape of the Weibull distribution, is presented with procedures given to obtain the coefficients which govern the distribution peakedness. Normalized non-dimensional frequency and period spectra were recommended for engineering applications for both reef and offshore locations. A zero up-crossing spectrum (ZUS) constructed from the zero upcrossing heights and periods is defined and compared with the Fourier spectrum. Also discussed are the benefits and disadvantages of the ZUS, particularly for non-linear wave environments in shallow water. Both the ZUS and Fourier spectra are used to test the adequacy of formulae which estimate individual wave parameters. Cross spectra analysis was made to obtain gain function and squared coherency for time series between two adjacent positions. It was found that the squared coherency is close to unity near the peak frequency. This means that the output time series can be predicted from the input by applying the gain function. However, the squared coherency was extremely small for other frequencies above 0.25 H2.

scholarly journals Shape Analysis of Cumulative Probability Density Function of Radiocarbon Dates Set in the Study of Climate Change in the Late Glacial and Holocene

Radiocarbon ◽  
2004 ◽  
Vol 46 (2) ◽  
pp. 733-744 ◽  
Author(s):  
Danuta J Michczyńska ◽  
Anna Pazdur
Keyword(s):  
Organic Matter ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Late Glacial ◽  
Cumulative Probability ◽  
Large Set ◽  
Radiocarbon Dates ◽  
Frequency Distributions ◽  
The Holocene

We report on a statistical analysis of a large set of radiocarbon dates for reconstruction of paleoclimate. Probability density functions were constructed by summing the probability distributions of individual 14C dates. Our analysis was based on 2 assumptions: 1) The amount of organic matter in sediments depends on paleogeographical conditions; 2) The number of 14C-dated samples is proportional to the amount of organic matter deposited in sediments in the examined time intervals. We quantified how many dates are required to give statistically reliable results. As an example, 785 peat dates from Poland were selected. The dates encompassed the Holocene and Late Glacial period. All dates came from the Gliwice Radiocarbon Laboratory. Results were compared with other paleoenvironmental records. Detailed analysis of the frequency distributions showed that preferential sampling plays an important part in the shape determination. The general rule to take samples from locations where visible changes of sedimentation are apparent (e.g. from the top and the bottom of the peat layer) results in narrow peaks in the probability density function near the limits of the Holocene subdivision.

Microstructural Constitutive Equation for Sprain Analysis

2008 ◽  
Author(s):  
Zheying Guo ◽  
Raffaella De Vita
Keyword(s):  
Experimental Data ◽  
Probability Density Function ◽  
Constitutive Equation ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Damage Evolution ◽  
Linear Elastic ◽  
Proposed Model ◽  
Collagenous Tissues

A new constitutive equation is presented to describe the damage evolution process in parallel fibered collagenous tissues such as ligaments and tendons. The model is formulated by accounting for the fibrous structure of the tissues. The tissue’s stress is defined as the average of the collagen fiber’s stresses. The fibers are assumed to be undulated and straighten out at different stretches that are defined by a Weibull probability density function. After becoming straight each fiber is assumed to be linear elastic. Its waviness is defined by a Weibull distribution. Tissue’s damage is assumed to occur at the fiber level and is defined as a reduction in the fiber’s stiffness. The proposed model is validated by using experimental data published in the biomechanics literature by Provenzano et al. [1].

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