Concomitants of Order Statistics from Gumbel's Bivariate Weibull Distribution

1997 ◽  
Vol 47 (3-4) ◽  
pp. 133-140
Author(s):  
Anjuman A. Begum ◽  
A. H. Khan
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Order Statistics ◽  
Density Function ◽  
Concomitants Of Order Statistics ◽  
Single Moments ◽  
Ordered Statistics ◽  
Probability Density Function Pdf ◽  
Bivariate Weibull Distribution

The probability density function (pdf) of the rth, 1 ≤ r ≤ n and joint pdf of the rth and sth, 1 ≤ r < s ≤ n, concomitants of ordered statistics are derived for Gumbel's bivariate Weibull distribution and their single moments are obtained. Also their means and variances are tabulated.

Concomitants of Order Statistics from Marshall and Olkin's Bivariate Weibull Distribution

2000 ◽  
Vol 50 (1-2) ◽  
pp. 65-70 ◽  
Author(s):  
Anjuman A. Begum ◽  
A. H. Khan
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Order Statistics ◽  
Density Function ◽  
Subject Classification ◽  
Concomitants Of Order Statistics ◽  
Ordered Statistics ◽  
Probability Density Function Pdf ◽  
Bivariate Weibull Distribution

The probability density function (pdf) of the rth, 1 ≤ r ≤ n, concomitants of ordered statistics are derived for Marshall and Olkin's bivariate Weibull distribution and their moments are obtained. Also their means and variances are tabulated. AMS (2000) Subject Classification: 62E15, 62G30.

scholarly journals Concomitant of Order Statistics from New Bivariate Gompertz Distribution

2020 ◽  
Vol 18 (2) ◽  
pp. 2-20
Author(s):  
Sumit Kumar ◽  
M. J. S. Khan ◽  
Surinder Kumar
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Order Statistics ◽  
Density Function ◽  
Generating Function ◽  
Moment Generating Function ◽  
Exact Expression ◽  
Gompertz Distribution ◽  
The Mean ◽  
Probability Density Function Pdf

For the new bivariate Gompertz distribution, the expression for probability density function (pdf) of rth order statistics and pdf of concomitant arising from rth order statistics are derived. The properties of concomitant arising from the corresponding order statistics are used to derive these results. The exact expression for moment generating function (mgf) of concomitant of order rth statistics is derived. Also, the mean of concomitant arising from rth order statistics is computed using the mgf of concomitant of rth order statistics, and the exact expression for joint density of concomitant of two non-adjacent order statistics are derived.

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 Dynamic Reliability Analysis Method of Degraded Mechanical Components Based on Process Probability Density Function of Stress

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Peng Gao ◽  
Liyang Xie
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Solar Array ◽  
Dynamic Reliability ◽  
Reliability Models ◽  
Practical Engineering ◽  
Mechanical Components ◽  
Reliability Computation ◽  
Probability Density Function Pdf

It is necessary to develop dynamic reliability models when considering strength degradation of mechanical components. Instant probability density function (IPDF) of stress and process probability density function (PPDF) of stress, which are obtained via different statistical methods, are defined, respectively. In practical engineering, the probability density function (PDF) for the usage of mechanical components is mostly PPDF, such as the PDF acquired via the rain flow counting method. For the convenience of application, IPDF is always approximated by PPDF when using the existing dynamic reliability models. However, it may cause errors in the reliability calculation due to the approximation of IPDF by PPDF. Therefore, dynamic reliability models directly based on PPDF of stress are developed in this paper. Furthermore, the proposed models can be used for reliability assessment in the case of small amount of stress process samples by employing the fuzzy set theory. In addition, the mechanical components in solar array of satellites are chosen as representative examples to illustrate the proposed models. The results show that errors are caused because of the approximation of IPDF by PPDF and the proposed models are accurate in the reliability computation.

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 A new subgrid-scale representation of hydrometeor fields using a multivariate PDF

2016 ◽  
Author(s):  
Brian M. Griffin ◽  
Vincent E. Larson
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Vertical Velocity ◽  
Lognormal Distribution ◽  
Large Eddy Simulations ◽  
Subgrid Scale ◽  
Microphysical Process ◽  
Large Eddy ◽  
Probability Density Function Pdf

Abstract. The subgrid-scale representation of hydrometeor fields is important for calculating microphysical process rates. In order to represent subgrid-scale variability, the Cloud Layers Unified By Binormals (CLUBB) parameterization uses a multivariate Probability Density Function (PDF). In addition to vertical velocity, temperature, and moisture fields, the PDF includes hydrometeor fields. Previously, each hydrometeor field was assumed to follow a multivariate single lognormal distribution. Now, in order to better represent the distribution of hydrometeors, two new multivariate PDFs are formulated and introduced. The new PDFs represent hydrometeors using either a delta-lognormal or a delta-double-lognormal shape. The two new PDF distributions, plus the previous single lognormal shape, are compared to histograms of data taken from Large-Eddy Simulations (LES) of a precipitating cumulus case, a drizzling stratocumulus case, and a deep convective case. Finally, the warm microphysical process rates produced by the different hydrometeor PDFs are compared to the same process rates produced by the LES.

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.

PROBABILITY DENSITY FUNCTION CONTROL OF QUANTUM SYSTEMS

2011 ◽  
Vol 25 (17) ◽  
pp. 2289-2297 ◽  
Author(s):  
YI-FAN XING ◽  
JUN WU
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Quantum Control ◽  
Quantum Systems ◽  
Quantum Model ◽  
Control Engineering ◽  
Control Of Quantum Systems ◽  
Probability Density Function Pdf ◽  
Specific Control

This paper proposes a new method of controlling quantum systems via probability density function (PDF) control. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed for the general case and limited input energy, respectively. Unlike traditional quantum control methods, this method directly controls the probability distribution of the quantum state. It provides an alternative method for quantum control engineering.

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