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Quantile functions for bounded distributions

dquant.m function t = dquant(X,PX,U) determines the values of the quantile function for a simple random variable with distribution X , P X at the probability values in row vector U . The probability vector U is often determined by a random number generator.

function t = dquant(X,PX,U) % DQUANT t = dquant(X,PX,U) Quantile function for a simple random variable% Version of 10/14/95 % U is a vector of probabilitiesm = length(X); n = length(U);F = [0 cumsum(PX)+1e-12];F(m+1) = 1; % Makes maximum value exactly one if U(n)>= 1 % Prevents improper values of probability U U(n) = 1;end if U(1)<= 0 U(1) = 1e-9;end f = rowcopy(F,n); % n rows of Fu = colcopy(U,m); % m columns of U t = X*((f(:,1:m)<u)&(u<= f(:,2:m+1)))';
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dquanplot.m Plots as a stairs graph the quantile function for a simple random variable X . The plot is the values of X versus the distribution function F X .

% DQUANPLOT file dquanplot.m Plot of quantile function for a simple rv % Version of 7/6/95% Uses stairs to plot the inverse of FX X = input('Enter VALUES for X ');PX = input('Enter PROBABILITIES for X '); m = length(X);F = [0 cumsum(PX)];XP = [X X(m)];stairs(F,XP) gridtitle('Plot of Quantile Function') xlabel('u')ylabel('t = Q(u)') hold onplot(F(2:m+1),X,'o') % Marks values at jumps hold off
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dsample.m Calculates a sample from a discrete distribution, determines the relative frequencies of values, and compares with actual probabilities. Input consists of value andprobability matrices for X and the sample size n . A matrix U is determined by a random number generator, and the m-function dquant is used to calculate the corresponding sample values. Variousdata on the sample are calculated and displayed.

% DSAMPLE file dsample.m Simulates sample from discrete population % Version of 12/31/95 (Display revised 3/24/97)% Relative frequencies vs probabilities for % sample from discrete population distributionX = input('Enter row matrix of VALUES '); PX = input('Enter row matrix of PROBABILITIES ');n = input('Sample size n '); U = rand(1,n);T = dquant(X,PX,U); [x,fr]= csort(T,ones(1,length(T))); disp(' Value Prob Rel freq')disp([x; PX; fr/n]')ex = sum(T)/n; EX = dot(X,PX);vx = sum(T.^2)/n - ex^2; VX = dot(X.^2,PX) - EX^2;disp(['Sample average ex = ',num2str(ex),])disp(['Population mean E[X] = ',num2str(EX),]) disp(['Sample variance vx = ',num2str(vx),]) disp(['Population variance Var[X]= ',num2str(VX),])
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quanplot.m Plots the quantile function for a distribution function F X . Assumes the procedure dfsetup or acsetup has been run. A suitable set U of probability values is determined and the m-function dquant is used to determine corresponding values of the quantile function. The results are plotted.

% QUANPLOT file quanplot.m Plots quantile function for dbn function % Version of 2/2/96% Assumes dfsetup or acsetup has been run % Uses m-function dquantX = input('Enter row matrix of values '); PX = input('Enter row matrix of probabilities ');h = input('Probability increment h '); U = h:h:1;T = dquant(X,PX,U); U = [0 U 1]; Te = X(m) + abs(X(m))/20;T = [X(1) T Te];plot(U,T) % Plot rather than stairs for general case gridtitle('Plot of Quantile Function') xlabel('u')ylabel('t = Q(u)')
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Questions & Answers

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Jyoti Reply
I only see partial conversation and what's the question here!
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what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
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I think
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what is the stm
Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
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what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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biomolecules are e building blocks of every organics and inorganic materials.
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research.net
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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