scholarly journals Definite Probabilities from Division of Zero by Itself Perspective

2020 ◽  
pp. 1-26
Author(s):  
Wangui Patrick Mwangi
Keyword(s):  
Probability Distribution ◽  
Negative Binomial ◽  
Random Variable ◽  
Distribution Functions ◽  
Point Of View ◽  
Basic Knowledge ◽  
Probability Distribution Functions ◽  
New Findings ◽  
Wide Range ◽  
New Finding

Over the years, the issues surrounding the division of zero by itself remained a mystery until year 2018 when the mystery was solved in numerous ways. Afterwards, the same solutions provided opened many other doors in academic space and one of the applications is in sure probabilities. This research is all about the sure probabilities computed from the zero divided by itself point of view. The solutions obtained in the computations are in harmony with logic and basic knowledge. A wide range of already existing probability distribution functions has been applied in different scenarios to compute the sure probabilities unanimously and new findings have also been encountered along the way. Some of the discrete and continuous probability distribution functions involved are the binomial, hypergeometric, negative binomial, Poisson, normal and exponential among others. It has been found in this work that sure probabilities can be evaluated from the division of zero by itself perspective. Another new finding is that in case of combinatorial, if the numerator is smaller than the denominator, then the solutions tend to zero when knowledge in gamma functions, integrations and factorials is applied. Again, if the case of continuous pdf involves integration and random variable specified in the direction of the parameter, then indirect computation of such probabilities should be applied. Finally, it has been found that the expansion of the domains of some of the parameters in some existing probability distribution functions can be considered and the restriction in conditional probabilities can be revised.

GENERALIZED EXCITED NEGATIVE BINOMIAL STATES OF ELECTROMAGNETIC FIELD AND SOME OF THEIR NON-CLASSICAL PROPERTIES

2003 ◽  
Vol 17 (07) ◽  
pp. 1071-1086 ◽  
Author(s):  
H. H. SALAH ◽  
M. DARWISH ◽  
A.-S. F. OBADA
Keyword(s):  
Electromagnetic Field ◽  
Correlation Function ◽  
Probability Distribution ◽  
Wigner Function ◽  
Coherent States ◽  
Negative Binomial ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
New States ◽  
Q Function

New states of electromagnetic field, generalized excited negative binomial states are introduced here. These states interpolate between the superposition of two excited coherent states and number states. The non-classical properties for these states are discussed, such as, second order correlation function, squeezing phenomena [normal squeezing and amplitude squared squeezing], phase properties in Pegg–Barnett formalism and the quasi-probability distribution functions (Q-function and Wigner function).

scholarly journals Analysis of Sonic Effects of Music from a Comprehensive Datasets on Audio Features

2021 ◽  
Vol 20 (1) ◽  
pp. 43-53
Author(s):  
Tobechukwu Okechukwu Otuokere ◽  
Agbotiname Lucky Imoize ◽  
Aderemi Aaron-Anthony Atayero
Keyword(s):  
Probability Distribution ◽  
Paper Analysis ◽  
Distribution Functions ◽  
Web Servers ◽  
Music Production ◽  
Probability Distribution Functions ◽  
Audio Features ◽  
Wide Range ◽  
Human Emotions

Music, for the longest time, has impacted human lives tremendously. The ability of music to access and activate a wide range of human emotions is sensational. Toward this end, audio features provide a variety of information necessary for sound engineers, music producers, and artists to improve their craft to excite the vast majority of music listeners across the globe. In this paper, analysis of audio features derived using the Spotify web API endpoint and Spotify (Python module for Spotify web servers) is presented. The dataset was curated from audio features of over 160,000 songs released from the year 1921-2020. For clarity, statistical descriptions and probability distribution functions of the audio features are reported. Also, the interrelationship and correlation amongst the various audio features are demonstrated. Overall, the dataset would find useful applications in classical and future music production.

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

<p>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 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) × 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.</p><p>[1] Valyrakis, M.; Alexakis, A. Development of a “smart-pebble” for tracking sediment transport. In Proceedings of the International Conference on Fluvial Hydraulics (River Flow 2016), St. Louis, MO, USA, 12–15 July 2016.</p><p>[2] Al-Obaidi, K., Xu, Y. & 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.</p><p>[3] Al-Obaidi, K. & Valyrakis, M. 2020, Asensory instrumented particle for environmental monitoring applications: development and calibration, IEEE sensors journal (accepted).</p>

Design for Project Change Management: Part 2 — Attribute Design

2004 ◽  
Author(s):  
D. Xue ◽  
S. Y. Cheing ◽  
P. Gu
Keyword(s):  
Optimal Design ◽  
Probability Distribution ◽  
Taguchi Method ◽  
Systematic Approach ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Construction Tasks ◽  
Design Attribute ◽  
Value Changes ◽  
Design Aspect

This research introduces a new systematic approach to identify the optimal design configuration and attributes to minimize the potential construction project changes. The second part of this paper focuses on the attribute design aspect. In this research, the potential changes of design attribute values are modeled by probability distribution functions. Attribute values of the design whose construction tasks are least sensitive to the changes of these attribute values are identified based upon Taguchi Method. In addition, estimation of the potential project change cost due to the potential design attribute value changes is also discussed. Case studies in pipeline engineering design and construction have been conducted to show the effectiveness of the introduced approach.

scholarly journals Using Percentiles to Communicate Snowfall Uncertainty

2014 ◽  
Vol 29 (5) ◽  
pp. 1259-1265 ◽  
Author(s):  
David R. Novak ◽  
Keith F. Brill ◽  
Wallace A. Hogsett
Keyword(s):  
Probability Distribution ◽  
False Alarm ◽  
Weather Prediction ◽  
Winter Precipitation ◽  
Risk Tolerance ◽  
Distribution Functions ◽  
Precipitation Forecast ◽  
Ensemble Forecasts ◽  
False Alarm Ratio ◽  
Probability Distribution Functions

Abstract An objective technique to determine forecast snowfall ranges consistent with the risk tolerance of users is demonstrated. The forecast snowfall ranges are based on percentiles from probability distribution functions that are assumed to be perfectly calibrated. A key feature of the technique is that the snowfall range varies dynamically, with the resultant ranges varying based on the spread of ensemble forecasts at a given forecast projection, for a particular case, for a particular location. Furthermore, this technique allows users to choose their risk tolerance, quantified in terms of the expected false alarm ratio for forecasts of snowfall range. The technique is applied to the 4–7 March 2013 snowstorm at two different locations (Chicago, Illinois, and Washington, D.C.) to illustrate its use in different locations with different forecast uncertainties. The snowfall range derived from the Weather Prediction Center Probabilistic Winter Precipitation Forecast suite is found to be statistically reliable for the day 1 forecast during the 2013/14 season, providing confidence in the practical applicability of the technique.

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