Questions tagged [probability-or-statistics]

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.

Filter by
Sorted by
Tagged with
4
votes
2answers
95 views

Commutation, symmetrizer and duplication matrices

The following 3 matrices are useful when viewing matrices as vectors, known as commutation $K_n$, symmetrizer $N_n$ and duplication $G_n$. They are usually defined by their matrix relations below. $$ \...
2
votes
3answers
340 views

Evaluate a certain three-dimensional constrained integral

The result of the three-dimensional integration ...
1
vote
1answer
91 views

Speeding up Gaussian expectations

I found that Mathematica's Expectation operator is slow for Gaussian random variables, I'd like to scale to 100 dimensions, but it currently takes 10 seconds for 10 dimensions, looking forward to tips ...
1
vote
0answers
40 views

Modeling geometric Brownian motion with an Ito process [closed]

I am trying to model geometric Brownian motion using ItoProcess. I am not sure why I am getting negative values in the output. I am not using ...
2
votes
1answer
101 views

Making animation based on COVID-19 data [closed]

There is an animation of the growth and spread of COVID-19 cases worldwide at http://www.healthmap.org/covid-19 My question is how do I make the same animation using Mathematica, also analyze the ...
1
vote
1answer
134 views

Probability poker game task

I have this task: And I've got this far in my mathematica program, however I can't figure out why my probability turns out 0? ...
1
vote
1answer
60 views

Expressions for moments of sample cumulants?

I sample $n$ points from standard normal and need the mean and variance of 3rd and 4th sample cumulants. @JimB suggested that variance of 4th sample cumulant is given by the expression below. This ...
1
vote
1answer
63 views

Help Calculating My “Deviation”

I created a "distribution deviation" where for $\left\{a_1,...,a_k\right\}$ we take all take the mean of all combinations of $\frac{\min\left\{a_{i},a_{j}\right\}}{\max\left\{a_{i},a_j\right\...
-1
votes
1answer
53 views

Can the WishartMatrixDistribution command be used for generating random density matrices?

I am interested in generating random members of two classes of $n \times n$ positive-definite matrices $A$ and $B$--the former symmetric in nature, the latter, Hermitian. The standard (Ginibre-matrix-...
1
vote
0answers
75 views

Calculate a nested integral

I wish to plot the following probability on Mathematica: $$ \pi=n\cdot\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty}\left[\int_{-\infty}^{z_{1}}G\left(z-z_{2}\right)\cdot f\left(z_{2}\right)dz_{2}\...
5
votes
1answer
152 views

Can this probability function speed be improved?

I have a process that as part of it requires a certain probability query, specifically, given a multinomial distribution with f equiprobable categories and r trials, some specific category has a given ...
0
votes
2answers
74 views

How to define a function of probability addition formula

In probability theory, the addition formula of any event is as follows: $$P(A \cup B)=P(A)+P(B)-P(A B)$$ $$\begin{aligned} P\left(A_{1} \cup A_{2} \cup \cdots \cup A_{n}\right)=& \sum_{i=1}^{n} P\...
4
votes
2answers
62 views

EstimatdDistribution returns evaluated expression, not function name/

Ok, this takes a little bit o preparation. I'd like to estimate a distribution for some data. I have a distribution function that is not part of the canonical Mathematica set so I define it via ...
0
votes
0answers
19 views

Defining the support of a random variable in Mathematica [duplicate]

I wish to create a Mathematica module that would take as input a Mathematica-defined probability distribution D and will perform an integration over the support of its density f, $supp(f)$ (where $f:X\...
0
votes
0answers
30 views

Problem with FormulaLookup and FormulaData

I'm not getting an answer when I type either: FormulaLookup["BinomialDistribution"] or ...
1
vote
1answer
47 views

How to use the function `Covariance` to calculate covariance correctly?

Note: The following questions are from the 23th question of the 2005 Chinese Graduate Mathematical Entrance Examination (first set): Suppose $X_{1}, X_{2}, \cdots, X_{n}(n>2)$ is a simple random ...
2
votes
1answer
57 views

How meaningful, or useful, are parameter errors produced when perfroming an unweighted LinearModelFit or NonlinearModelFit?

This may be a question which teeters on the brink of belonging more to the realm of statistics and Cross-Validated SE, but I'm also specifically interested in Mathematica fitting routines. Usually, if ...
-2
votes
2answers
64 views

How to find the expectation of the following complex probability distribution?

I want to find the expectation of the random variable UV. But the following code doesn't return the desired result: ...
0
votes
1answer
69 views

Confusion about the correlation coefficient [closed]

If a wooden stick with a length of 1 meter is randomly cut into two sections, what is the correlation coefficient of the length of the two sections? ...
-4
votes
1answer
111 views

How to calculate the expectation and variance of a complex probability distribution

Assuming that the continuous random variables X1 and X2 are independent of each other, and the variances exist, the probability ...
0
votes
0answers
20 views

Getting MatrixPropertyDistribution::sclrvctr: error from documentation example

I'm new to StackExchange, but I am having a strange error using just downloaded Mathematica 12.1.1.0 (Student version). I'm trying to use the MatrixPropertyDistribution function, but Mathematica gives ...
1
vote
1answer
55 views

How to deal with more complex transformation distributions

Assume that X1, X2,..., Xn ($n\ge 2$) are simple random samples from a normal distribution $\mathrm{N}(\mu, 1)$, let $\overline{\mathbf{X}}=\frac{1}{\mathrm{n}} \sum_{i=1}^{\mathrm{n}} \mathrm{X}_{i}$....
0
votes
1answer
99 views

Change a list of x,y to a density function to analyze the distribution

So I have some (x,y) data from an oscilloscope. These numbers form a more or less gaussian shape. I am trying to extract the skewness of this shape, but the skewness functions only seem to accept ...
2
votes
1answer
44 views

What is the difference between the height specifications “PDF” and “Probability” for Histogram built-in function?

maybe this question is something conceptual but I need to clarify it. Given a data I can use Histogram to plot the distribution of the frequencies of the data. If I need the relative frequencies I ...
1
vote
1answer
30 views

Select a subsequence of a sequence according to tosses of a biased coin

I have a sequence, from which I would like to select a subsequence, each term of the original sequence being included in the subsequence with probability $p$, independently of the other terms. That is,...
0
votes
3answers
78 views

How to solve the approximate value of this probability problem

It is known that X1, X2,...,Xn are random samples from the population X, where the probability of X taking 0 or 1 is equal, that is, $P(X=0)=P(X=1)=\frac{1}{2}$. I want to find an approximation of $P\...
3
votes
2answers
165 views

Hypothesis testing with LogLikelihood methods in Mathematica

I'm trying to understand Likelihood methods and hypothesis. To this end I am trying to construct small examples that I can play with. Let's say I have some data which I know (or suspect follows the ...
0
votes
2answers
78 views

Does MMA have a maximum likelihood estimation function?

I want to use MMA to solve question 23 in this post: The English translation of this question is as follows: Let the probability density function of population $X$ be $f\left(x, \sigma^{2}\right)=\...
0
votes
1answer
57 views

Problem plotting expression involving Generalized hypergeometric functions $_2F_2 \left(.,.,. \right)$

I'm trying to plot a graph for the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]=a 2^{-\frac{\kappa }{2}-1} b^{-\frac{\kappa }{2}} \theta ^{-\kappa } \...
1
vote
1answer
87 views

Confidence interval

With data = {{0.002, 2.51053}, {0.004, 2.54217}, {0.006, 2.55543}, {0.008, 2.54247}}; I obtain a linear fit 2.51038 + 5.454 x; ...
6
votes
3answers
456 views

Multivariate linear regression

Say I have a 4-dimensional data set with two independent variables x1, x2, and two dependent variables y1, y2, i.e. each row is <...
2
votes
1answer
73 views

Why doesn't this function TransformedDistribution work?

According to the information in this post, we know that ${\displaystyle z={\sqrt {-2\ln U_{1}}}\cos(2\pi U_{2})}$ follows a normal distribution, and the datas generated supports this view. ...
0
votes
2answers
166 views

How to use MMA to simulate the German tank problem

In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without replacement. In simple terms, suppose there ...
2
votes
1answer
90 views

How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
1
vote
1answer
47 views

How to compute summary statistics and quantiles of user defined discrete distribution? [closed]

I am interested to find out the mean, median, Variance, Skewness, Kurtosis and Quantiles of the following discrete distribution with pmf (E^((1 - E^[Nu]) n) [Nu]^x BellB[n, x])/x! with x=0,1,2...... ...
1
vote
0answers
55 views

Computing expected value of multinomial variables

We consider a two-dimensional dicrete probability distribution on $\mathcal{X} \times \mathcal{Y}$ with $|\mathcal{X}|\cdot |\mathcal{Y}| = r \cdot q$ distinct values with corresponding probabilities $...
3
votes
1answer
92 views

Smooth Kernel Distribution

I have 20060 dates and I used the SmoothkernelDistribution function to get a distribution of them: However, I also need a functional form of the distribution to use it in another program without use ...
0
votes
2answers
53 views

How to get a list of exponentially distributed points sampled in a range

I want to get 256 points exponentially sampled in a range, and then get its histogram. If I plot PDF, I get the following: ...
2
votes
1answer
116 views

FindDistribution[] with error bars? (And a ChiSquared Question)

I've got some data defined as follows: ...
12
votes
2answers
867 views

How to solve the Monty Hall problem?

Problem For purely recreational purposes I would like to solve the Monty Hall problem with Mathematica using the function Probability (dedicated to the calculation ...
0
votes
0answers
88 views

How to calculate and plot the joint distribution probability density function of independent variables

Knowing that X and Y are independent of each other and follow the standard normal distribution, I want to know how to find and ...
1
vote
2answers
105 views

Expectation of product of independent random variables (using Expectation function)

I'm trying with no luck to get Expectation to calculate the expectation of expressions containing sums of products of independent random variables. For instance, ...
1
vote
1answer
99 views

How to use Quartiles to work the same as TI-83 calculator? [closed]

The statistics book I am using defines quartiles the same as Method 1 explained in wikipedia. Use the median to divide the ordered data set into two-halves. If there is an odd number of data points ...
4
votes
2answers
135 views

Calculate combined standard deviation

If I have a data that I fit with NonlinearModelfit that fits a data based on two fitting parameters, c1 and ...
0
votes
0answers
42 views

How to calculate with right probabilities values?

My code solves the equation G(Ht) using random p probabilities for each value of d in my <...
2
votes
1answer
48 views

Confidence interval considering the division of 2 means with different CIs? Statistics

I have the mean and its confidence interval (standard deviation and size of its sample) of 2 different data A and B. I want to divide A/B and get the confidence interval of its division. Is there a ...
1
vote
1answer
46 views

Using NIntegrate to reproduce NProbability over joint Gaussian distribution

Consider a random vector {s,c} with a bivariate normal distribution. For a vector of positive scalars {a, ß, σz}, I'm interested ...
2
votes
3answers
59 views

Contribution of 3 groups of data to an overall PDF

I have a time series that is comprised of 3 subgroups. I want to know how I can calculate the contribution of each of these subgroups to the overall PDF. ...
0
votes
1answer
51 views

Gaussian Integral incorrect

I'm trying to learn about the Gaussian Normal distribution using Mathematica. So I defined my Gaussian like this ...
3
votes
1answer
56 views

Domain of ProbabilityDistributions

I am trying to do some symbolic statistics. Is there a way to get the Domain of a distribution? Like this ...

1
2
3 4 5
30