Questions about systematic data collection and organization, or the application of probability theory to model the inherent patterns and properties of sampled data, underlying data distribution(s) or random processes.

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4
votes
0answers
59 views

Does Mathematica have built-in support for multivariate regression?

I know that LinearModelFit can generate a model of a single response variable as a function of a set in input variables. Does Mathematica provide support for ...
1
vote
0answers
33 views

Training Hidden Markov Models using Mathematica

I have created a Hidden Markov Process with an initial probability vector, emission and transmission matrices. ...
3
votes
3answers
147 views

How do I define a two point random variable?

How do I define a random variable $X$ such that $Pr[X=x_1]=p_1$ and $Pr[X=x_2]=p_2$ where the values $x_i$, $i=1,\,2$ are just symbols and the probabilities $p_i$, $i=1,\,2$ are symbolic expressions ...
0
votes
0answers
26 views

How to get the numerical result of inverse CDF?

This is my code. And I want to solve the function which contains both Q and L. But Mathematica only gives me a result with "InverseCDF" function, but not a number? I'm not sure whether I use the code ...
1
vote
3answers
241 views

How to fit a Distribution to data that already looks like a distribution?

I have a set of data that is already ordered as a distribution. Here is a picture worth 999 words: I tried FindDistributionParameters, and ...
1
vote
1answer
130 views

How to calculate the probability exactly

I random chioce three points from unit disk.I want to calculate the probability exactly that they circumcircle is contained within the unit disk still.Of curse,we can use the Monte Carlo to estimate ...
2
votes
1answer
100 views

$\log_q \log_q$ plot instead of $\log \log$ plot

By defining the $\log_q$ as: $$ \log_q(x)=\frac{x^{1-q}-1}{1-q}, x \geq 0, q \neq 1$$ how would it be possible to have the equivalent of the LogLogPlot command, ...
4
votes
2answers
141 views

How to calculate this probability?

Here I want to find the probability $p$ which is given by $$p=\int_0^{r_d}\mathcal{L}_I(\beta r^{\alpha}|r)f_R(r)dr$$ with $r_d=1$ and $0 \le r\le r_d$. I want to calulate the probability for ...
0
votes
1answer
55 views

Power spectrum density calulation with ARProcess

I have a measurement of $x$ coordinates of an oscillating particle at presence of noise taken at constant time steps of 1/60 s. The corresponding data set can be obtained here: http://goo.gl/...
7
votes
4answers
951 views

How to draw a hanging rootogram in Mathematica?

I am trying to plot a hanging rootogram of some data in Mathematica. I can't seem to find a built in function for it, while simply using Histogram (on "transformed" data) does not seem to plot what I ...
9
votes
1answer
238 views

Random walk on a Sierpinski gasket

I am trying to simulate a random walk on a Sierpinski gasket. The best strategy i could come up with is to use Nearest point function to determine the next possible step of my walker. But this creates ...
4
votes
1answer
503 views

How to perform convolutions on this complicated pdf?

For a known pdf f[x], I need to calculate integrals over the probability density of the sum of Log[f[x]] over independent samples: $$Q[t,n]\equiv P(\sum_{i=1}^{n}...
0
votes
0answers
51 views

Improving kernel density estimation of statistical PDF from measured CDF

I'm trying to use WeightedData and SmoothKernelDistribution to generate a PDF from measured points along a CDF. I've tried to ...
4
votes
1answer
114 views

How to apply BinCounts to weighted data

For example, I have an array: data = {1, 2, 3, 4, 5, 6, 7, 8, 9} and a corresponding list of weighting factors ...
0
votes
1answer
53 views

Using LinearModelFit, how can I test the hypothesis $\beta=c$ with $c\neq 0$?

Assuming a simple linear model $y=x\beta+u$, is there a way to test the hypothesis $\beta=c$ with $c\neq 0$, using the LinearModelFit?
1
vote
1answer
46 views

Using distribution of data instead of data in `EstimatedDistribution`

Because of huge amount of data, the data saved in their frequency. for example {1,1,1,1,1,1,2,2,1,2,2,1,1,2,1,2,1,3,24} saved as ...
1
vote
1answer
90 views

package for calculating exponent of power law distribution

There are some packages to fitting power law to empirical date in "R", "matlab", "python" Here with maximum likelihood method As it said here. Does it exist similar package in Mathematica?
6
votes
2answers
133 views

Can Mathematica help me win my on-line game?

I've become addicted to the Forge of Empires web browser game. Presently, the game has a special event going on, which is in commemoration of the 2016 EUFA Soccer Championship. The event has a set ...
3
votes
1answer
53 views

TransformedDistribution using integration with parameter doesn't work

I would like to ask for kind help with a following problem using TransformedDistribution in Mathematica. First here is the beginning of the code, that works: ...
2
votes
1answer
79 views

Algorithm for determining factorability

Consider the following polynomial : $P[x,y]:=a_{11}+a_{12}y+a_{13}y^2+a_{21}x+a_{22}x y+a_{23}x y^2+a_{31}x^2+a_{32}x^2 y+a_{33}x^2 y^2$ where the $a_{ij}$ are either $1$ or $-1$. Thus there are $...
3
votes
1answer
72 views

ITO Process with random initial position

I am trying to define an ITO process with random initial state but its only drawing once an uses it for all paths. Here is the code: ...
3
votes
1answer
68 views

The permutation of given number sequence that has specific correlation with another

I am interested in the relationship between the Pearson correlation coefficients and the permutations of two random number sequences. An initial Mathematica study is as below: ...
1
vote
2answers
74 views

Modeling Gaussian Distribution for 4 Variables

I have 4 random variables A,B,C,D, that all have the same variance $\sigma^2$, but they are independent of each other. What I am trying to find, or to at least approximate, is the standard deviation ...
3
votes
2answers
130 views
3
votes
1answer
61 views

Looking for a convenient way to replace a large data sample with an analytic approximation

Suppose that data is a large data sample, and that Histogram[data] produces a very smooth-looking distribution. Since ...
1
vote
3answers
79 views

API for defining parametric probability distributions

Mathematica has a lot of machinery for working with predefined probability distributions. It is not clear how to make that machinery work with a new distribution. Suppose I want to define a brand new ...
-1
votes
1answer
158 views

Why MMA is not able to solve this problem? [closed]

I am running these following code in Mathematica. But, MMA does not output anything. It is giving me an message as "The integrand .... has evaluated to non-numerical values for all sampling points in ...
3
votes
0answers
53 views

PearsonChiSquareTest for count/frequency data?

I read with interest a previous question on the PearsonChiSquareTest from a few years ago, and one answer was very helpful: Performing a chi-square goodness of fit ...
8
votes
1answer
111 views

What is ExpectationE and what does it do?

I just found the symbol ExpectationE with autocomplete. Rendered the symbol is Searching the documentation and the internet leads to nothing. Does somebody ...
0
votes
1answer
48 views

Experiment to test Infinite monkey theorem [closed]

I need to apply this experiment: For all numbers between [0,128] let be t {set total=0 repeat this experiment n times {set start=0 choose random number [0,255] lets be R While(R!=t) {...
6
votes
3answers
245 views

Creating a custom distribution with specified skew and kurtosis

Let's say I want to create a simulated sample of returns for a given investing/trading strategy. I know that my strategy is profitable on 64% of trades, that the ratio of mean win / mean loss is 0.72, ...
2
votes
2answers
129 views

Expected area of random triangle

I want to check the following theorem by using Mathematica: $\textbf{Theorem} $. If three point $P,Q,R$ are picked independently at random in the triangle $ABC$, than expected value of the area of ...
0
votes
0answers
32 views

Evaluating the cumulative multivariate hypergeometric distribution

Suppose there are 5 black, 10 white, and 15 red marbles in an urn for a total of $N=5+10+15$ marbles. You randomly draw $n=6$ marbles without replacement. The probability that you pick exactly two of ...
0
votes
1answer
39 views

Is it the correct syntax with TransformedDistribution?

I define a function as f[x_] := ...;which is in fact the PDF of a random variable $X$. The PDF if given by $f_X(x)$. Let $Y$ is a random variable, which is the ...
1
vote
1answer
154 views

How can I evaluate a certain probability density function?

The PDF of a random variable $X$ is given by Note that $H(t)$ is also a function of $x$. Here $-\infty<\mu<\infty$, $\lambda>=0$ and $m>=1/2$ Let $I$ be a function of random variable $Y$....
9
votes
3answers
247 views

Deriving a PDF for an annulus distribution

I would like to derive the PDF for an ''annulus'' type distribution, defined by the parameters $\theta\sim U(0,2 \pi)$ and $d\sim N(0,\sigma)$; where $\theta$ is the angle round a circle of radius $r$,...
7
votes
1answer
51 views

KaryTree of Text .csv and Correlation

How can I make a KaryTree of this raw-data (raw-data at the end of the question): This is is data from a political survey in which I ask 5 questions with the following possible answers: Q1: 'Y'= ...
1
vote
0answers
34 views

How to calculate Probability of “Ranking”? [closed]

I took a course with other 10 students. After the final exam, the professor reported statistical result of scores to us: 1. The range of score: 46~98; 2. The average score: 73.3; 3 The S.D of score: ...
1
vote
0answers
82 views

How to “INJECT” with holding Evaluation, specifically into a WhenEvent

I am importing a set of differential and stochastic equations from an external package, and want to use Mathematica to analyse this. I am struggling building the set of equations that I can use with <...
1
vote
2answers
65 views

MMA gives error when a different PDF expression is used for the same distribution

I have the following MMA code. Note that the function I declared at the very beginning is the PDF of square of a Nakagami Distributed random variable. With $m=1$ and $P=1$, $f(h)$ becomes Exponential ...
0
votes
1answer
61 views

How to find this probability with PDF from TransformedDistribution?

I need to find the expression for the following equation, where $m>0$ ...
7
votes
3answers
244 views

Simulation with two random walkers on a lattice with periodic boundaries

I am having some difficulties implementing a Monte Carlo simulation in order to compare the results to analytical calculations. The following code simulates a case with one random walker and a ...
3
votes
2answers
143 views

Finding mean of data sets with unequal length

I have two data sets on the form (x,y) of unequal length: ...
0
votes
1answer
70 views

How to generate samples from an arbitrary continuous pdf?

If I define an arbitrary pdf p[x_] for a arbitrary-dimensional continuous variable x, how can I use Mathematica to create a function that will return a set of n random samples of x with distribution p?...
-1
votes
1answer
129 views

Periodic boundary conditions for two walkers

For some reason I'm getting infinite loops most of the time i run this. Perhaps the periodic boundary conditions are wrong. Seems like the probability of the two positions to be the same is extremely ...
6
votes
1answer
71 views

Bug (or missed opportunity) in MarginalDistribution?

Observe: dist = MultivariateHypergeometricDistribution[k, Range@5]; Tr@Range@5 MarginalDistribution[dist, {1}] MarginalDistribution[dist, {1, 2}] First@% 15 ...
7
votes
1answer
135 views

Vertexes possibility estimate in graph

I have graph which represents runner race events. Vertex means runner, edge means running event between runners, edge weight is how much more seconds runner won running race against opponent. (running ...
0
votes
1answer
47 views

Plot bivariate data with marginals using Graphics3D [duplicate]

I have some 2D data (a load of random walks) that I would like to show using a bivariate line plot with marginals attached (I would like the output to look similar to that in this question.) The ...
1
vote
1answer
42 views

Difference between two usages of TransformedDistribution

I am modeling the distribution of the sum of two dice throws as a TransformedDistribution ...
4
votes
1answer
122 views

PDF of product of two random variable with PDFs involving Dirac-delta function

I am trying to find the PDF of product of two random variables with the following distributions, ...