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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3
votes
1answer
35 views

Probability Generating Function(s)?

I'm very new to Mathematica and I have started to use it since I have been tackling some Physics related problems(I'm an engineer by training). Specifically, I'm dealing with Master Equations and one ...
5
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3answers
174 views

Plotting a normal curve over a histogram

I am teaching a basic introduction to normal curves, and the textbook introduces the topic with the idea of rolling five dice and recording the sum. Do this many times and create a histogram of the ...
3
votes
2answers
81 views

Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance (in a $(n+1)$-dimensional space) between two points selected uniformly at random on a unit $n$-...
1
vote
1answer
30 views

How to find the inverse of CDF of geometric function? [closed]

The cdf of geometric distribution is given by $ F(x)=1-(1-p)^x$. I want to calculate the inverse of it, for example, $F^{-1}(U)$ I am doing the following ...
2
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3answers
88 views

Estimate the expected distance between two random points on the unit $n$-sphere [duplicate]

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance in a $(n+1)$-dimensional space between two points selected uniformly at random on the unit $n$-sphere? ...
1
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2answers
65 views

TransformedDistribution of normal and skew-normal distributions

I have the following distributions: distC =NormalDistribution[251.563, 0.317394] distS =SkewNormalDistribution[252.973, 0.503173, 5.59741] I want to analyse what ...
1
vote
1answer
42 views

Implementing Random process for exponential correlation function

I'm trying to simulate a random process for a variable $-1<X(t)<1$ with average 0, i.e., $\left\langle X(t)\right\rangle =0$ and correlation $\left\langle X(t)X(0) \right\rangle \propto e^{-t/\...
1
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0answers
20 views

Consistency of sample quantile to population quantile for discrete variables [closed]

Can I know if the sample quantile converges to the population quantile in probability for discrete variables? If we use Hoeffding (1963)'s results, is this true?
3
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1answer
69 views

Evaluating expected improvement in Mathematica

There is a concept in optimization called expected improvement where you sequentially search for the value of x that optimizes the problem. Here is a screen shot of the general idea of the derivation: ...
1
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0answers
59 views

Solving $E[abXab]=Y$ for Gaussian $(a,b)$

I have $d/2$-dimensional variables $a,b$ jointly distributed as Gaussian($\mu,\Sigma$) in $d$ dimensions, and need to solve the following equation for $X$ $$E[ab^TXab^T]=Y$$ This is equivalent to ...
0
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1answer
42 views

Defining a Gaussian mixture distribution for $N$ number of Gaussian distributions

I am experimenting a bit with mixed-Gaussian distributions. If I want to define a mixture of two or three distributions, I do this with: ...
2
votes
2answers
148 views

Raising the normal distribution curve to a specified height on the $y$-axis

I'd like to know how to fit the normal distribution curve between $x$ and $y$ values so that the curve maintains its bell shape. I guessed the sigma is the scale ratio, but it doesn't work as I ...
0
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1answer
81 views

Find the probability (relative volume) of a certain 4-ball with respect to Hilbert-Schmidt measure

Let us consider the set of points {x,y,z,1-x-y-z} and impose the strict ordering constraint ...
0
votes
1answer
79 views

How to solve the Summation equation by FindRoots [closed]

I want to find out the value of alpha and lambda where u lies between 0 and 1.
-1
votes
2answers
43 views

using exponential distribution to solve a half life problem [closed]

i have information about the half life of a certain element. the half life is 29 years. i need to calculate how much of this material is left if we start counting from 1954, which was 66 years ago. i ...
-3
votes
1answer
103 views

Is it a bug in TransformedDistribution?

I worked with ...
2
votes
1answer
71 views

trying to solve for mean and standard deviation using Normcumdist and Solve [closed]

I am trying to find values for the mean and standard deviation of a normal distribution with these characteristics. $\qquad P(X \le 90) = 0.96$ $\qquad P(X \le 50) = 0.3$ I am trying to do this using <...
0
votes
0answers
42 views

Find custom distribution parameters that best fit the PDF/CDF data histograms

I have the probability and cummulative density histograms of some data. I need to find the parameters of a custom distribution that best fit the data. For probability distributions included in ...
0
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0answers
40 views

Performance inconsistency: What's going on here?

Consider: ...
0
votes
2answers
49 views

How to make calculations involving symbolic summation?

I want to minimize a function involving the sum of $n$ fixed (but indetermined) $x$ values, for example: Minimize[Sum[(x[i] - a)^2, {i, 1, n}], a] Expected answer: ...
0
votes
1answer
25 views

multivariate Gaussian distribution with identity covariance

I want to draw Geometry (or contours) for multivariate Gaussian distribution with identity covariance matrix (or draw decision boundary). How this is possible via Wolfram's online at Here? Please ...
2
votes
0answers
35 views

Failure in MultinormalDistribution

My RandomVariate fails to evaluate when sampling from a multinormal distribution, any idea what's happening here? This is Mathematica 12.1 on Mac: ...
2
votes
3answers
85 views

What is the probability of the digit $k$ in the number $x^n$

Well, the title of the question says it all: how to write a code that finds the probability of the digit $k$ in the number $x^n$? For example, when $x=2$, $n=100$, and $k=7$ we are trying to find how ...
1
vote
1answer
96 views

Fisher information for a Gaussian [closed]

I would like to calculate the Fisher information for $f(x|\alpha)=\frac{1}{(2\pi \delta^2(\alpha))^{1/2}} Exp\{-\frac{(x-\mu(\alpha))^2}{2\delta^2(\alpha)}\}$ using ${\rm FisherInformation}[\{\mu, \...
0
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1answer
48 views

Fisher distribution expressed with Chi ²

I am learning about the ANOVA test. This involves the Fisher-distribution. I know there is the ANOVA function and the ...
1
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0answers
28 views

Speed up exact distribution of the sum of the top $k$ statistics on a bounded discrete uniform distribution?

I came across a nice answer by Sasha (I believe a Wolfram engineer) on mathematics stack exchange regarding the distribution of the sum of the top $k$ order statistics. (This was an answer to an RPG ...
6
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4answers
1k views

Mean age of people [closed]

I have the following datas: I want to find mean age by using following formula, Any way to do this in general in Mathematica easily.
1
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0answers
40 views

Computing the Mean of Around Values

I understand the computation of the uncertainty of independent Around values to be based on the following first order approximation $$ \delta f(x,y)=\sqrt{\left(\frac{\text{$\delta $f}}{\partial x}...
1
vote
1answer
64 views

i need to simulate a roulette table where a perosn bets $10 on red 1 time, 5 times,20 times, 100 times and 10,000 times

I need to simulate a roulette table where a perosn bets $10 on red 1 time, 5 times,20 times, 100 times and 10,000 times, i then need to find out how much the person wins or loses once they play 10,000 ...
2
votes
1answer
55 views

Intepreting the results of DistributionFitTest, and other alternatives in Mathematica 12.1

I have been playing with DistributionFitTest as a means of testing how normal some data sets I have. I've been working with some simulated data sets so I can try ...
0
votes
0answers
45 views

Mann Whitney Test

I am trying to check data in Mathematica with the Mann Whitney Test. The author states: Mann–Whitney's U-test; U = 609, z = 2.07, p < 0.05. How would I put this ...
1
vote
1answer
156 views

How to plot this pdf

Let $x\sim N(\mu,\sigma^2)$ and $y=\max\{e^{x-1}-\kappa,0\}$. How to get and plot the pdf of y? In particular, there will be a probability mass at $y=0$, which is a nondifferentiable point. I tried <...
1
vote
1answer
55 views

Generating a set of random variates from Poisson distribution

Say I am not allowed to use built-in PoissonDistribution, which means I should generate 100 random numbers first, and then with these 100 random numbers to generate 100 random variates from Poisson ...
3
votes
3answers
117 views

How to simulate the roll of 3 or more dice and ask for a sum of 3 or more?

How to simulate the throwing of 3 or more dice and ask for the sum of 3 or more and indicate the number of calves, or more that are produced. For example if you throw 3 dice, how many cases will add ...
1
vote
2answers
172 views

Confirm and possibly simplify a 2009 result for a 2D constrained integration

This is a direct descendant of two other recent questions, 3D and Equivalence, both of which have been answered in skillful, interesting manners. (See also the comment [actually answer] of JimB to ...
0
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0answers
36 views

Piecewise function inside ProbabilityDistribution causing errors

I'm using a complicated Piecewise function to create a probability distribution and draw random points from it. ...
1
vote
1answer
49 views

How to emulate statistical command choice tab of this widget?-how to do what i ask?

I designed this little program, but I want you to be able to choose what I want to look for by choosing it as you do with the widget tab, please help me. widget Widget of internet my program ...
1
vote
1answer
46 views

Probability distribution with random paremeters

Is it possible to set something like this? A probability distribution with random parameters ...
0
votes
0answers
28 views

Unable to evaluate expectation of sum, but able to evaluate expectation of each summand

I would like to evaluate the expectation of the expression x + x Log[x] where x follows a generalised gamma distribution ...
2
votes
1answer
82 views

Turning a matrix matrix into a probability table

I want to build a probability table that is able to answer questions such as "if i roll 5, 4 sided dice what is the probability i get at least a 16?" My current code is: ...
1
vote
1answer
127 views

Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities

In a recent posting, TwoQubits user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
1
vote
0answers
32 views

Adding a module to teach Mathematica the Laplace transform of particular Mittag-Leffler functions

Mathematica 11.3 is not aware of a useful Laplace transform LaplaceTransform[t^(-a) MittagLefflerE[a, a, t^a], t, s] which for ...
0
votes
0answers
32 views

Plot the confidence interval bands from standard error and mean

My data has 20 horizons of mean and standard error. The very first step I'd like to manually calculate the 95% confidence interval from standard error and mean. After this, is to plot the timevarying ...
6
votes
2answers
73 views

Ideas to speed up an order statistic calculation?

A toy example: {n, top} = {25, 100}; mxs = RandomReal[{0, top}, n]; dist = UniformDistribution[Thread[{0, mxs}]]; result = Mean[OrderDistribution[dist, n]] With ...
3
votes
2answers
186 views

Simplifying the code to calculate probability of tossing 4 unfair dice

Four identical unfair dice are tossed once. Find the probability of events in which the sum of numbers (facing up) is 18. Given the probability of face 6 is $1/2$ and that of each other face is $1/10$....
2
votes
1answer
62 views

Concatenation of Distributions

I would like to calculate mean, variance, ... of a concatenation of distributions (is this the correct technical term?). For an easy example I am trying to calculate the mean of a PoissonDistribution ...
1
vote
0answers
27 views
0
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0answers
41 views

Total Variation Distance(between Gaussians)

I am interested in a tool that calculates the total variation distance between two multivariate Normal distributions. Any help will be much appreciated as I am a complete beginner.(So far, I have ...
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. $$ \...

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