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 Performance Analysis Of Cooperative Relaying In Nakagami-M Fading Channels

1970 ◽  
Vol 6 (2) ◽  
pp. 1-5
Author(s):  
B Barua ◽  
MZI Sarkar
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Fading Channels ◽  
Generating Function ◽  
Error Probability ◽  
Moment Generating Function ◽  
Cooperative Relaying ◽  
Relay Network ◽  
Symbol Error Probability

This paper is concerned with the analysis of exact symbol error probability (SEP) for cooperative diversity using amplify-and-forward (AF) relaying over independent and non-identical Nakagami-m fading channels. The mathematical formulations for Probability Density Function (pdf) and Moment Generating Function (MGF) of a cooperative link have been derived for calculating symbol error probability with well-known MGF based approach taking M-ary Phase Shift Keying (MPSK) signals as input. The numerical results obtained from this research have been compared with different fading conditions. It is observed that the existence of the diversity link in a relay network plays a dominating role in error performance. Keywords: Symbol Error Probability; Probability Density Function; Moment Generating Function; Nakagami-m fading. DOI: http://dx.doi.org/10.3329/diujst.v6i2.9338 DIUJST 2011; 6(2): 1-5

scholarly journals A probablistic proof of the series representation of the MacDonald function with applications

1998 ◽  
Vol 21 (3) ◽  
pp. 463-466
Author(s):  
M. Aslam Chaudhry ◽  
Munir Ahmad
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Generating Function ◽  
Open Problem ◽  
Series Representation ◽  
Moment Generating Function ◽  
Macdonald Function

A series representation of the Macdonald function is obtained using the properties of a probability density function and its moment generating function. Some applications of the result are discussed and an open problem is posed.

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.

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.

Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod Response

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Giuseppina Autuori ◽  
Federico Cluni ◽  
Vittorio Gusella ◽  
Patrizia Pucci
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Coefficient Of Variation ◽  
Fractional Laplacian ◽  
Numerical Procedure ◽  
Elastic Rod ◽  
The Mean ◽  
Distributed Forces ◽  
Nonlinear Fashion

In this paper, we yield with a nonlocal elastic rod problem, widely studied in the last decades. The main purpose of the paper is to investigate the effects of the statistic variability of the fractional operator order s on the displacements u of the rod. The rod is supposed to be subjected to external distributed forces, and the displacement field u is obtained by means of numerical procedure. The attention is particularly focused on the parameter s, which influences the response in a nonlinear fashion. The effects of the uncertainty of s on the response at different locations of the rod are investigated by the Monte Carlo simulations. The results obtained highlight the importance of s in the probabilistic feature of the response. In particular, it is found that for a small coefficient of variation of s, the probability density function of the response has a unique well-identifiable mode. On the other hand, for a high coefficient of variation of s, the probability density function of the response decreases monotonically. Finally, the coefficient of variation and, to a small extent, the mean of the response tend to increase as the coefficient of variation of s increases.

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 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.

On the linear exponential family

1968 ◽  
Vol 64 (2) ◽  
pp. 481-483 ◽  
Author(s):  
J. K. Wani
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Scalar Product ◽  
Exponential Family ◽  
Characterization Theorem ◽  
Random Variable ◽  
Moment Generating Function ◽  
The Moment ◽  
Image Position

In this paper we give a characterization theorem for a subclass of the exponential family whose probability density function is given bywhere a(x) ≥ 0, f(ω) = ∫a(x) exp (ωx) dx and ωx is to be interpreted as a scalar product. The random variable X may be an s-vector. In that case ω will also be an s-vector. For obvious reasons we will call (1) as the linear exponential family. It is easy to verify that the moment generating function (m.g.f.) of (1) is given by

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