Items tagged with distribution

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.

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

10

 

100

(1)

# Unnormalized Probability distrubution

f := (x,y,z) -> exp(-x^2 -y^2 - z^2);

proc (x, y, z) options operator, arrow; exp(-x^2-y^2-z^2) end proc

(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;

XYZ := Matrix(100, 3, {(1, 1) = 9.758694699049908, (1, 2) = 2.6237746853802246, (1, 3) = 5.657441459582465, (2, 1) = -6.591359538862333, (2, 2) = -2.89852696242302, (2, 3) = 3.875752299737945, (3, 1) = -4.844154988559739, (3, 2) = 9.940065432132954, (3, 3) = -9.803954954738758, (4, 1) = -2.0640136273371272, (4, 2) = -5.516570020337457, (4, 3) = 6.864266760210192, (5, 1) = -8.52010460846124, (5, 2) = 3.049021459372298, (5, 3) = 8.446639955925516, (6, 1) = 3.68192133924018, (6, 2) = 2.099812838165187, (6, 3) = 5.41908441347849, (7, 1) = -1.9522333460767616, (7, 2) = -2.2550913703373006, (7, 3) = -9.146802881299026, (8, 1) = 9.65670402787902, (8, 2) = -7.156256814189918, (8, 3) = -2.4362772589956228, (9, 1) = -1.9563202955503058, (9, 2) = -9.497300285795937, (9, 3) = 4.086792489667353, (10, 1) = 2.4134389439915687, (10, 2) = -1.5777549246951743, (10, 3) = 4.590260910092939, (11, 1) = -6.912603890414553, (11, 2) = -6.317994211449776, (11, 3) = -5.514458586709711, (12, 1) = -2.3730959111105605, (12, 2) = 4.515505349389063, (12, 3) = -4.618905364532699, (13, 1) = -6.777320563012783, (13, 2) = -2.592746269696038, (13, 3) = 3.4606233000823785, (14, 1) = 5.162248626548372, (14, 2) = 6.831201749364123, (14, 3) = -.45015604546277466, (15, 1) = 7.422222438307784, (15, 2) = 4.684593823866264, (15, 3) = 2.4743282533488493, (16, 1) = -2.9844651022821473, (16, 2) = 1.4205174564875769, (16, 3) = -5.2711013471817925, (17, 1) = 3.710714174950745, (17, 2) = -6.462898847493945, (17, 3) = -6.457524910033669, (18, 1) = -4.117027324643008, (18, 2) = 9.147680451914468, (18, 3) = 6.592867713951691, (19, 1) = .6125860771377116, (19, 2) = -4.693559276141599, (19, 3) = 5.338433358705297, (20, 1) = 6.648467725703679, (20, 2) = 8.491617904792019, (20, 3) = 8.68956546236539, (21, 1) = 1.9498038374515865, (21, 2) = -5.52459190605918, (21, 3) = -7.842221898312729, (22, 1) = -3.2937733858950775, (22, 2) = -2.5287238471471003, (22, 3) = -6.355449887978885, (23, 1) = -4.015499533337867, (23, 2) = -8.249993008468286, (23, 3) = -8.01809435155083, (24, 1) = -.9481491686135186, (24, 2) = 2.802330964934301, (24, 3) = -.20472396153106232, (25, 1) = -1.5470869355907517, (25, 2) = -6.387662244937832, (25, 3) = -6.13509339062259, (26, 1) = -2.8078736405552878, (26, 2) = -9.098977850528517, (26, 3) = 7.917831475851365, (27, 1) = 1.1663839973859425, (27, 2) = 4.4634695836619045, (27, 3) = -8.01820700636371, (28, 1) = 4.850907314038782, (28, 2) = -3.051247088364198, (28, 3) = -9.116688564746777, (29, 1) = -1.5133043274861873, (29, 2) = 3.2123364900580764, (29, 3) = 1.145903116095237, (30, 1) = -1.4128842284758996, (30, 2) = -2.322627978560572, (30, 3) = 5.449901343752481, (31, 1) = -7.502544825603743, (31, 2) = 2.5469300488693403, (31, 3) = -3.7611988500746225, (32, 1) = -9.511319678992521, (32, 2) = -9.567003707393871, (32, 3) = -6.420350413713298, (33, 1) = -4.196294697385456, (33, 2) = 8.21139977046057, (33, 3) = -3.220886435045635, (34, 1) = -3.6495883420154733, (34, 2) = 6.011173125576221, (34, 3) = -5.7970872591289595, (35, 1) = 3.0738026793295035, (35, 2) = 4.916949686854423, (35, 3) = .20305039530500402, (36, 1) = 9.138718481413683, (36, 2) = 6.262256272215215, (36, 3) = 8.127286465304294, (37, 1) = 8.71461745569761, (37, 2) = -2.3338736274894156, (37, 3) = 2.578478773046358, (38, 1) = -.8422733229126642, (38, 2) = 2.345584646328984, (38, 3) = -7.969322223753757, (39, 1) = -5.190432063358308, (39, 2) = 1.5098971940562773, (39, 3) = -2.1829049454729077, (40, 1) = 5.277958885729566, (40, 2) = .6010340953003119, (40, 3) = -8.907667695526849, (41, 1) = 5.186547662621926, (41, 2) = -4.498604883561299, (41, 3) = 0.25658264064304603e-1, (42, 1) = 4.812961299572285, (42, 2) = -5.027420806760592, (42, 3) = -1.3655765623150558, (43, 1) = 4.87376682974652, (43, 2) = -.9672245909605444, (43, 3) = 9.951206990243783, (44, 1) = -7.881591665344693, (44, 2) = -5.445743479469048, (44, 3) = 6.232051619906457, (45, 1) = 3.631208609406313, (45, 2) = 6.0889916722614, (45, 3) = -.2869666020396462, (46, 1) = -.7347884281256167, (46, 2) = 9.722084837919404, (46, 3) = 7.888955111347865, (47, 1) = -5.756735894901313, (47, 2) = -9.4001609946122, (47, 3) = -7.249068104658704, (48, 1) = -8.029625246237833, (48, 2) = .7132838133447539, (48, 3) = -2.1999017110942916, (49, 1) = 6.471489478556769, (49, 2) = -8.258455601982153, (49, 3) = 8.547124499962496, (50, 1) = -6.499805252358408, (50, 2) = 6.04182881111608, (50, 3) = 8.34987664832234, (51, 1) = -6.728601804300136, (51, 2) = 9.782898194006798, (51, 3) = 4.271480231886315, (52, 1) = 3.319744328222212, (52, 2) = -8.661074832044998, (52, 3) = 2.3667476724388, (53, 1) = 7.887787507084855, (53, 2) = 8.787967237690697, (53, 3) = -3.1342421951730914, (54, 1) = .33116416702540796, (54, 2) = -9.636449327266085, (54, 3) = 8.720546533795396, (55, 1) = 4.054046139009506, (55, 2) = 3.6767722749271066, (55, 3) = -7.504519186790148, (56, 1) = -6.9281924676119955, (56, 2) = 5.674729601664373, (56, 3) = 4.611707230114142, (57, 1) = 9.069141397724955, (57, 2) = .6827513576545652, (57, 3) = 2.929548648516276, (58, 1) = .8176816248295289, (58, 2) = 7.7071890186228345, (58, 3) = 6.663039713385899, (59, 1) = 3.594677964209339, (59, 2) = 7.980097978122803, (59, 3) = -2.034355435624491, (60, 1) = -9.268739639030944, (60, 2) = 2.518752521609917, (60, 3) = 4.9964441872127185, (61, 1) = 6.184077025875865, (61, 2) = -7.242620151748835, (61, 3) = 6.70441020956261, (62, 1) = 4.972377435523942, (62, 2) = -5.6439681257575085, (62, 3) = -3.5507920527548116, (63, 1) = -7.596259640258387, (63, 2) = -6.357178482191326, (63, 3) = 1.0452323371671, (64, 1) = .5009032952521757, (64, 2) = -9.163602720540913, (64, 3) = 9.582582648677842, (65, 1) = -3.483327424735016, (65, 2) = -7.86116682899586, (65, 3) = .9861706603660547, (66, 1) = .9289887980613702, (66, 2) = 2.328869701713703, (66, 3) = -3.391527807867945, (67, 1) = -2.0223849523360204, (67, 2) = 8.793220203221335, (67, 3) = 2.389431103555598, (68, 1) = -1.6981322677390676, (68, 2) = -2.910885380653423, (68, 3) = -2.7872685799559456, (69, 1) = -6.3852447949041125, (69, 2) = -1.7874181988097213, (69, 3) = 5.130190870038886, (70, 1) = -4.892265190238985, (70, 2) = 9.68698833968903, (70, 3) = -1.7219850261962062, (71, 1) = -9.589284506836309, (71, 2) = 8.911583780705254, (71, 3) = -.15309791230124503, (72, 1) = 8.473512252408145, (72, 2) = 3.532893568670783, (72, 3) = 3.8948646626522017, (73, 1) = 3.073997780165058, (73, 2) = 9.766045246265726, (73, 3) = 9.454677701595681, (74, 1) = 8.652271440971283, (74, 2) = 5.336627744331885, (74, 3) = -3.4449007901318645, (75, 1) = -6.729752629449488, (75, 2) = -3.2660147121704775, (75, 3) = 6.756063661571513, (76, 1) = 8.42194511784395, (76, 2) = 3.2476372079896247, (76, 3) = 4.781444545470562, (77, 1) = 5.893157707775064, (77, 2) = -5.116694264194415, (77, 3) = 9.083489127590862, (78, 1) = 1.5478839341329742, (78, 2) = -4.089854983368064, (78, 3) = -9.361547409920432, (79, 1) = -1.1992880847949277, (79, 2) = 3.6035674246100413, (79, 3) = -2.8626202763491593, (80, 1) = -4.8477252657512455, (80, 2) = .5569366083759579, (80, 3) = 3.25307668574429, (81, 1) = 5.038927877349, (81, 2) = -1.7681297318493083, (81, 3) = -4.369968817030188, (82, 1) = -5.426610357889972, (82, 2) = 2.0527643607279433, (82, 3) = -5.392338653650725, (83, 1) = -8.716258252162028, (83, 2) = 5.010401118474713, (83, 3) = 4.222571023606502, (84, 1) = 5.346590215531489, (84, 2) = 1.6706634852391726, (84, 3) = 2.4914583398661705, (85, 1) = 3.4240437071307106, (85, 2) = 1.0358502987193496, (85, 3) = 1.8121730583927196, (86, 1) = 4.304250295716802, (86, 2) = 1.6714123751542882, (86, 3) = 3.2087593262520375, (87, 1) = 2.8412165686770443, (87, 2) = .236398399169504, (87, 3) = -9.04890653772268, (88, 1) = -1.6190341275023385, (88, 2) = -8.348145460026013, (88, 3) = -3.0243038297988223, (89, 1) = -2.184758355916509, (89, 2) = 4.391402697189795, (89, 3) = -.9731883928851364, (90, 1) = 6.322802057506454, (90, 2) = 9.923122225937387, (90, 3) = -5.181900057597786, (91, 1) = -3.6514427268830074, (91, 2) = -2.909313900861563, (91, 3) = 4.300900265923531, (92, 1) = 6.290795458013026, (92, 2) = 9.425176303668113, (92, 3) = 7.123645840125757, (93, 1) = 5.7814702987791655, (93, 2) = -3.071024773992807, (93, 3) = -4.369846097628933, (94, 1) = 7.045277806876914, (94, 2) = 7.730877235206126, (94, 3) = 4.621016594474829, (95, 1) = .11273235143512395, (95, 2) = -.9061027001618438, (95, 3) = -7.244742149609673, (96, 1) = 2.7132277772275373, (96, 2) = -1.7314542195836946, (96, 3) = 6.734455634994351, (97, 1) = 9.017888307562703, (97, 2) = -5.645358632853991, (97, 3) = -7.2279656851528, (98, 1) = -1.1207168996237922, (98, 2) = -7.486908252747475, (98, 3) = 1.7641877077898727, (99, 1) = -8.799623604410481, (99, 2) = -3.821708128663694, (99, 3) = -2.6768639909012437, (100, 1) = 7.334997939986373, (100, 2) = 4.522088633296637, (100, 3) = 6.135190893222113}, datatype = float[8])

(3)

ScatterPlot3D(XYZ, color = blue, symbolsize = 20);

 

 

 

 

 


 

Download Sample_Test.m

 

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

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?

Thanks in advance

 

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.

Thanks in advance.

taro

 

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

DensityPlot(X,filled=true)

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

 

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 ?

of a (concrete/general) triangle, making use of Maple tools in an efficient way?  Mathematica applies the barycentric coordinates and the Dirichlet distribution to this end. More generally, how to efficiently choose a random point in a given bounded region?

Is there a difference between these two? 

with(Statistics):

Sample(Normal(0,1),100)

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

 

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

Dear all

I have downloaded a third party Maple package from following link:

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.

If anybody have an idea about this format "tar.gz" please help me out.

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

 

 

I am trying to find the pdf of the inverse of a random variable X, that represents a distribution I defined. I currently have : 

with(Statistics):
T:=Distribution(PDF=(x->piecewise(0<x and x<1,1/4,3<x and x<5,3/8,0)));
X:=RandomVariable(T);
PDF(X,u);
CDF(X,u);
Y:=1/X;
T1:=RandomVariable(Y);

but this seems to be incorrect as I get a message saying T1:=RandomVariable(Y) is being passed a wrong argument. 

What is the right way to obtain the pdf of 1/X?

 

Hi,

 

  Suppose I have a probability distribution function f(x). I would like to generate points in a 

(1) given interval, can be up to infinity

(2) number of points

(3) satisfy the known probability distribution function f(x)

(4) possible other specifications

 

 

  Is there any build-in option in maple I could use? Or I have to write something manually?

 

Thank you very much!

 

This should be trivial but I am not able to figure out the right syntax to execute it

The pdf is given by :

f_X(x)={ 1/25 *x, 0<=x<5

             2/5 -x/25, 5<=x<10

             0, otherwise

I have tried to use the "CumulativeDistributiveFunction" so far

1 2 3 4 Page 1 of 4