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## Weibull Distribution Formula...

What is the Maple Formula for the Excel function: =WEIBULL.DIST(A1,2,6.2,FALSE)

where A1..A26 is 0..26  ?  How do I plot it?

Thank you, Les

## Customized discrete random variables...

Hi everyone,

I seek for creating a discrete random variable with the following characteristics. Let i be an integer between 1 and 100. The random variable is an integer, among i-x, i-x+1, i-x+2..., i-1, i+1, i+2... i+x. For example, with i=20 and x=5, the random variable is an integer between 15 and 25; with i=23 (and again x=5), the random variable is an integer between 18 and 28; and with i=98, the random variable is an integer among 93, 94... 97 and then 99, 100, 1, 2, 3.

Each possible value has the same probability, that is, 1/2x.

Any tips? Thank you in advance.

## Inverse CDF of the Standard Normal Distribution...

Is there a command in Maple to produce a table of z values given F(z) where F is the CDF of the Standard Normal Distribution? I know of the command ProbabilityTable to generate a table of z, F(z) values.  What I would really like is F, Inv(F) table of values. I guess  I could write my own code to do this but was wondering if there is an easier way to do this.

## Determine the distribution function on resulting o...

Hello! Prompt please as in Maple can determine the distribution function of the resulting histogram distribution? I know about cdf function, but how to act in relation to the histogram do not know.

Histogram:

```restart;
with(stats);
with(stats[statplots]);
data2 := [30, 30.5, 31, 31.5, 32, 32.5, 32.6, 33, 33.1, 33.3, 33.6, 34, 35, 36];
histogram(data2, area = count);```

In other words, I need smoothing the histogram, get graph and get on it to obtain an analytical expression.

## Sampling from multivariate probability distributio...

Hi All,

I have a fucntion f(x,y,z) = exp(-x^2 -y^2 - z^4) and would like to plot the probabity density in real space. One method would be to randomly sample points in a grid based on f(x,y,z). The function f(x,y,z) is clearly peaked around x=y=z=0, so you would expect many points to lie around there. So the plot would look like a clump near (0,0,0) which gets less dense away from (0,0,0).

In the worksheet below, I sampled points from the Uniform distribution to file in the 3d-plot. I would like these points to be sampled from f instead, but am not sure how to do this.

Any help is appreciated,

 > restart;
 > with(Statistics):
 > R := 10; # x-axis size N := 100; # Number f points to sample
 (1)
 > # Unnormalized Probability distrubution f := (x,y,z) -> exp(-x^2 -y^2 - z^2);
 (2)
 > # Clearly f is peaked at (0,0,0) and decays. Therefore I want a plot a lot of points near (0,0,0), and fewer points away from (0,0,0) plot3d(f(x,y,0), x = -1..1, y = -1..1);
 > X := Sample(Uniform(-R, R), N):
 > Y := Sample(Uniform(-R, R), N): Z := Sample(Uniform(-R, R), N): XYZ := Matrix([[X], [Y], [Z]])^%T;
 (3)
 > ScatterPlot3D(XYZ, color = blue, symbolsize = 20);
 >
 >
 >
 >

## Please some help for the better study of number of...

I wish to study the trend of medical consultations each day during six years. Thus I expect near 2200 datas to analyse.

But some parameters are to consider :

- I don't have yet the datas per day, but the mean is about 2 consultations per day

- as it is difficult to do more than 3 or perhaps 4 consultations during one day (9h30 am - 13h pm), the others if they exist will probably be seen the next day (aso if the next day 3 news consultations occured)

- then, I don't know actually (as I expect the datas or each day but don't have now these datas) if the better distribution will be simply follow a Poisson' law, or exponential, or negative binomial, ..

- do someone have a clue for the better law given what i said ?

Further, I don't have a stastic program especially used for time trend, excepting Systran 13, but I don't believe that this program can be used with a theoric model of distribution, I recall that it does usual tasks, autocorrelations, saisonnal adjustments, .. but with continuous distributions I believe, and a linear model (removing the basic frequencies)

As such program (study of temporal series) is usually sold about 3000\$ in France, that I don't expect to be a trader, with only one calculus to do, could anyone tell me how to adjust the better model to the 2200 datas that could be expected ?

Thx for your help, friendly yours;

Milos

## How to sample correlated Random Variables?...

Hi everyone,

I've not been able to figure this one out. Say I have an expression dependant on two random variables, like this:

C:=A+B

where A and B are randomvariables, each following a specific distribution.

If I ask for a Sample of C

Sample(C,1)

Maple will sample A, sample B and compute C. But say that A and B are correlated (with a cc of 0.8). How do I define this?

## distributing limit to each terms...

Hello people in mapleprimes,

I want to distribute limit or Limit to each terms of summation.

Limit(f(a+h)-f(a),h=0);

But, the output is not distributed one, but the same as the input, though

I want it to become Limit(f(a+h),h=0)+Limit(f(a),h=0), or

Limit(f(a+h),h=0)+f(a).

Isn't there any way for it, other than a trivial one that is

subs(Limit(f(a+h)-f(a),h=0)=Limit(f(a+h),h=0)+Limit(f(a),h=0),Limit(f(a+h)-f(a),h=0));

?

I hope someone will teach me.

taro

## Fill a distribution plot...

with(Statistics):
X := RandomVariable(Normal(0, 1))

DensityPlot(X,filled=true)

I don't know why the plot doesn't produce a shaded plot.

## Why does Mean fail with it?...

Below is a custom distribution created based on a function that takes a parameter.

It is possible to create the custom distribution e.g. as D1 and then use it afterwards to find e.g. Mean, but it is not possible to call Mean directly with the creation of the distribution in the call.

Why is that ?

## RandomVariable vs Distribution in Sample?...

Is there a difference between these two?

with(Statistics):

Sample(Normal(0,1),100)

Sample(RandomVariable(Normal(0, 1)), 100)

## How to generate a normal distribution around given...

How to generate a random normal distribution of points around the point [3,15] for example?

## Maple package in "tar.gz" format...

Dear all

http://cpc.cs.qub.ac.uk/summaries/AEQP_v1_0.html

The distribution format is  "tar.gz", but I don't know what to with this format, that how should I load this package into Maple library. I have window 8.1.

## Error in Distribution...

Hi,

I have the following input

***

restart;
with( Statistics ):

a:=2;c:=0.3;
g:= exp(-a*x) + c*a*exp(-a*x);
#f := x -> piecewise( x < 0, 0, x>0, g );
f :=x -> piecewise( x < 0, 0, x>0, exp(-a*x) + c*a*exp(-a*x));

norm_factor:=int( f(x), x=0..infinity );
print(norm_factor);

randomize():
F := Distribution( PDF = 1/norm_factor*f ):
X := RandomVariable( F ):

N := 20;
S := convert( Sample(X,N), list );

print(`cc`,S[1]);

***

The code works. However, if I comment out

f :=x -> piecewise( x < 0, 0, x>0, exp(-a*x) + c*a*exp(-a*x));

, then use

f := x -> piecewise( x < 0, 0, x>0, g );

i.e.

f := x -> piecewise( x < 0, 0, x>0, g );
#f :=x -> piecewise( x < 0, 0, x>0, exp(-a*x) + c*a*exp(-a*x));

It is said "

Error, (in Statistics:-Sample) unable to construct the envelopes for _R, try to specify the initial range"

The norm_factors are actually the same for both inputs. What is the reason for the error message?  Suppose I still want to use something like

f := x -> piecewise( x < 0, 0, x>0, g );

,how to fix the problem?

Thank you very much