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.

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58 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-...
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0answers
83 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
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1answer
157 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 ...
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2answers
78 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\...
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2answers
66 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 ...
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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\...
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30 views

Problem with FormulaLookup and FormulaData

I'm not getting an answer when I type either: FormulaLookup["BinomialDistribution"] or ...
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1answer
65 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 ...
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1answer
71 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 ...
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2answers
69 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: ...
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1answer
77 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? ...
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1answer
197 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 ...
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0answers
22 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 ...
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1answer
58 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 $\overline{\mathbf{X}}=\frac{1}{\mathrm{n}} \sum_{i=1}^{\mathrm{n}} \mathrm{X}_{i}$....
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1answer
108 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
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1answer
52 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 ...
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1answer
33 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,...
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3answers
93 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
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2answers
173 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 ...
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2answers
100 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)=\...
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1answer
87 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 } \...
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1answer
101 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
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3answers
498 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
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1answer
86 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. ...
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2answers
210 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
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1answer
103 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,...
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1answer
53 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...... ...
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0answers
60 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
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1answer
137 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 ...
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2answers
59 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
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1answer
119 views

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

I've got some data defined as follows: ...
13
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3answers
1k 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 ...
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0answers
149 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 ...
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2answers
138 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, ...
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1answer
115 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
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2answers
166 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 ...
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0answers
43 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
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1answer
54 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 ...
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1answer
51 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
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3answers
63 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
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1answer
74 views

Gaussian Integral incorrect

I'm trying to learn about the Gaussian Normal distribution using Mathematica. So I defined my Gaussian like this ...
3
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1answer
62 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 ...
2
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1answer
96 views

How do I implement random selection in my code? [closed]

I would like to display the value of G[Ht], which is actually the sum of the equation Ht = (rt - c) d - f [d], but I am having ...
3
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2answers
70 views

Generate synthetic multi-dimensional data given its correlation and distribution

I am trying to create a synthetic dataset with 3 columns. I know the correlation between each pair of columns. How do I go about it? A search revealed this Copula distribution example, but it creates ...
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2answers
96 views

Finding a Distribution

I'm trying to find the optical distribution for the following data https://drive.google.com/file/d/1z_cSu7w8tlz_uEYHr8Y0fFBTwLNo4jtp/view?usp=sharing As there are a lot of points, the only way to ...
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0answers
30 views

Confusion about EstimatedProcess::ntsprt error

Given the data as follows, ...
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0answers
68 views

Deriving the maximum likelihood estimates for a multivariate Gaussian

I am new to Mathematica and wonder if anyone can give me skeleton of a solution to a simple problem that I will then modify for my purposes as so far I have not managed to properly grasp the syntax. ...
2
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3answers
159 views

Issues with ProbabilityDistribution

I am trying to specify a user-defined probability distribution with ProbabilityDistribution and am running into errors when I try to obtain the distribution ...
2
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0answers
31 views

Find at least one distribution with given parameters [closed]

There is a continuous probability distribution that I have only limited information about. I know that its PDF is a smooth unimodal function with exactly $2$ inflection points; I also know numeric ...
4
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1answer
209 views

RandomVariate cannot sample from a custom multivariate ProbabilityDistribution

Let us try to define 2D distribution through PDF: ...

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