On the conditional expected value of contributions from a renewal process

1966 ◽  
Vol 3 (2) ◽  
pp. 464-480 ◽  
Author(s):  
M. F. James
Keyword(s):  
Probability Distribution ◽  
Cross Sections ◽  
Renewal Process ◽  
Mean Value ◽  
Distribution Functions ◽  
Total Contribution ◽  
Probability Distribution Functions ◽  
General Terms ◽  
The Mean ◽  
Neutron Cross Sections

The problem discussed in this paper arose from the study of the effects of unresolved resonances on neutron cross-sections, but it is considered here in more general terms.Events in a modified renewal process occur at successive intervals x1, x2, …, and the ith event has associated with it a parameter Γi. The random variables xi and Γi are all independent, and their probability distribution functions are known. Each event contributes to two quantities F(u) and G(v) measured at u and v respectively. The value of the total contribution of all events to G(v) is assumed to be known from observation: this paper gives formulae for the mean value of F(u) conditional on this known value of G(v).

On the conditional expected value of contributions from a renewal process

1966 ◽  
Vol 3 (02) ◽  
pp. 464-480
Author(s):  
M. F. James
Keyword(s):  
Probability Distribution ◽  
Cross Sections ◽  
Renewal Process ◽  
Mean Value ◽  
Distribution Functions ◽  
Total Contribution ◽  
Probability Distribution Functions ◽  
General Terms ◽  
The Mean ◽  
Neutron Cross Sections

The problem discussed in this paper arose from the study of the effects of unresolved resonances on neutron cross-sections, but it is considered here in more general terms. Events in a modified renewal process occur at successive intervals x 1, x 2, …, and the ith event has associated with it a parameter Γ i . The random variables xi and Γ i are all independent, and their probability distribution functions are known. Each event contributes to two quantities F(u) and G(v) measured at u and v respectively. The value of the total contribution of all events to G(v) is assumed to be known from observation: this paper gives formulae for the mean value of F(u) conditional on this known value of G(v).

scholarly journals Global and Regional Comparison of Daily 2-m and 1000-hPa Maximum and Minimum Temperatures in Three Global Reanalyses

2009 ◽  
Vol 22 (17) ◽  
pp. 4667-4681 ◽  
Author(s):  
A. J. Pitman ◽  
S. E. Perkins
Keyword(s):  
Probability Distribution ◽  
Probability Density Functions ◽  
Distribution Functions ◽  
Maximum Temperature ◽  
Daily Maximum ◽  
Density Functions ◽  
Regional Comparison ◽  
Probability Distribution Functions ◽  
Air Temperatures ◽  
The Mean

Abstract A comparison of three global reanalyses is conducted based on probability density functions of daily maximum and minimum temperature at 2-m and 1000-hPa levels. The three reanalyses compare very favorably in both maximum and minimum temperatures at 1000 hPa, in both the mean and the 99.7th and 0.3rd percentiles of both quantities in most regions. At 2 m, there are large and widespread differences in the mean and 99.7th percentiles in maximum temperature between the three reanalyses over land commonly exceeding ±5°C and regionally exceeding ±10°C. The 2-m minimum temperatures compare unfavorably between the three reanalyses over virtually all continental surfaces with differences exceeding ±10°C over widespread areas. It is concluded that the three reanalyses are generally interchangeable in 1000-hPa temperatures. The three reanalyses of 2-m temperatures are very different owing to the methods used to diagnose these quantities. At this time, the probability distribution functions of the 2-m temperatures from the three reanalyses are sufficiently different that either the 2-m air temperatures should not be used or all three products should be used independently in any application and the differences highlighted.

scholarly journals THE STUDY OF THE DEPENDENCE OF SIZES OF MEASURED MICROSCOPIC OBJECTS AT THE POSITION OF THE SLICE PLANE

2019 ◽  
Vol 27 (4) ◽  
pp. 55-60
Author(s):  
A. E. Lun'kov ◽  
U. A. Gladilin ◽  
K. E. Ibragimova
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Cross Sections ◽  
Mean Value ◽  
Distribution Functions ◽  
Distribution Law ◽  
The Mean ◽  
The Cross ◽  
The Difference ◽  
The Given

For microscopic objects in the form of spheres of different radii have been calculated the functions of distribution of the cross sections radii, taking into account the dependence on the position of the plane of the slice. Taking into account this dependence, the distribution functions of the cross sections radii of the spheres whose radii were given by the normal distribution law with the variation of its parameters were calculated. It is found that the difference between the given distribution function of the radii of spheres and the distribution function of their sections in the plane of the slice depends on the ratio of the standard deviation to the mean value of the radii. Depending on this relation, two simple algorithms are proposed to reconstruct the distribution function of the radii of objects by the distribution function of the radii of their sections. It is shown that these algorithms can be used to correct the experimental curve of the size distribution of micro-objects in the form of ellipsoid.

Peak Wind Power Statistics

1990 ◽  
Vol 112 (3) ◽  
pp. 170-173 ◽  
Author(s):  
B. Alibe
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Gaussian Process ◽  
Wind Power ◽  
Wind Velocity ◽  
Distribution Functions ◽  
Stationary Gaussian Process ◽  
Probability Distribution Functions ◽  
Mean Wind Speed ◽  
The Mean

Probability distribution functions, mean upcrossing rates and other descriptors are developed for the power that can be potentially extracted from the wind. Wind power is proportional to the cube of the wind velocity. The wind velocity is modeled as a stationary Gaussian process. The distribution of the extreme power is developed from mean upcrossing rates and the assumption that crossings of high thresholds follow a Poisson probability law. The results obtained are valid for any amount of the mean wind speed.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

Probability Distribution Functions for the Random Forced Burgers Equation

1997 ◽  
Vol 78 (10) ◽  
pp. 1904-1907 ◽  
Author(s):  
Weinan E ◽  
Konstantin Khanin ◽  
Alexandre Mazel ◽  
Yakov Sinai
Keyword(s):  
Probability Distribution ◽  
Burgers Equation ◽  
Distribution Functions ◽  
Probability Distribution Functions

Exploring probability distribution functions best-fitting the kinetic energy of coarse particles at above threshold flow conditions

2021 ◽  
Author(s):  
Hamed Farhadi ◽  
Manousos Valyrakis
Keyword(s):  
Probability Distribution ◽  
Kinetic Energy ◽  
Test Section ◽  
Particle Transport ◽  
River Flow ◽  
Distribution Functions ◽  
Transport Processes ◽  
Flow Conditions ◽  
Probability Distribution Functions ◽  
Transport Regime

&lt;p&gt;Applying an instrumented particle [1-3], the probability density functions of kinetic energy of a coarse particle (at different solid densities) mobilised over a range of above threshold flow conditions&amp;#160;conditions corresponding to the intermittent transport regime, were explored. The experiments were conducted in the Water Engineering Lab at the University of Glasgow on a tilting recirculating flume with 800 (length) &amp;#215; 90 (width) cm dimension. Twelve different flow conditions corresponding to intermittent transport regime for the range of particle densities examined herein, have been implemented in this research. Ensuring fully developed flow conditions, the start of the test section was located at 3.2 meters upstream of the flume outlet. The bed surface of the flume is flat and made up of well-packed glass beads of 16.2 mm diameter, offering a uniform roughness over which the instrumented particle is transported. MEMS sensors are embedded within the instrumented particle with 3-axis gyroscope and 3-axis accelerometer. At the beginning of each experimental run, instrumented particle is placed at the upstream of the test section, fully exposed to the free stream flow. Its motion is recorded with top and side cameras to enable a deeper understanding of particle transport processes. Using results from sets of instrumented particle transport experiments with varying flow rates and particle densities, the probability distribution functions (PDFs) of the instrumented particles kinetic energy, were generated. The best-fitted PDFs were selected by applying the Kolmogorov-Smirnov test and the results were discussed considering the light of the recent literature of the particle velocity distributions.&lt;/p&gt;&lt;p&gt;[1] Valyrakis, M.; Alexakis, A. Development of a &amp;#8220;smart-pebble&amp;#8221; for tracking sediment transport. In Proceedings of the International Conference on Fluvial Hydraulics (River Flow 2016), St. Louis, MO, USA, 12&amp;#8211;15 July 2016.&lt;/p&gt;&lt;p&gt;[2] Al-Obaidi, K., Xu, Y. &amp; Valyrakis, M. 2020, The Design and Calibration of Instrumented Particles for Assessing Water Infrastructure Hazards, Journal of Sensors and Actuator Networks, vol. 9, no. 3, 36.&lt;/p&gt;&lt;p&gt;[3] Al-Obaidi, K. &amp; Valyrakis, M. 2020, Asensory instrumented particle for environmental monitoring applications: development and calibration, IEEE sensors journal (accepted).&lt;/p&gt;

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