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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1answer
39 views

Set up a distribution in LogLikelihood that depends on data

I want to define a loglikelihood function to perform a fit of some data points to a function, like the following, but using the native LogLikelihood[] function. $ likelihood=\sum_{i}(Log{(\frac{1}{\...
4
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1answer
129 views

Third/Fourth derivative of cross-entropy loss

I need a nice formula for the third (or fourth derivative if it's easier) of cross-entropy loss $\frac{\partial^3 J}{\partial z^3}$ where $$J(p(z)) = -\sum_i q_i\log p(z)_i$$ $$p(z)_i=\frac{\exp z_i}{\...
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1answer
62 views

Outputting probability of rolling 6 dice N times, generating a new output each roll

I am looking to output the probability of n classic six-sided dice but I am not sure how to go about starting. This is what I have written out so far, but no way to go about accounting for n dice for ...
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1answer
102 views

Estimating parameters of a custom or constrained distribution

I am trying to estimate the parameters of a custom distribution (an approximation of the skew normal), but I can't get Mathematica to use DistributionFitTest, EstimatedDistribution, or ...
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2answers
90 views

Verifying probabilities equality by imposing conditions

I'd like to verify the following equality in Mathematica: $$ P(Z_1+Z_2=2,Z_1=1,Z_2=1)=P(Z_1=1,Z_2=1) $$ by knowing that $Z_1,Z_2 \in \lbrace 1,2,3,4 \rbrace$ are two independent and uniform random ...
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0answers
23 views

Express symbolic equation of KL Divergence between multivariate distribution succinctly in matrix form using Mathematica

I would like to express the KL Divergence between 2 multi-variate Gaussian distributions in matrix form. I am able to compute the symbolic form but it essentially gives the output fully simplified ...
2
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2answers
157 views

Can the CopulaDistributions be fitted?

This is an immediate follow-up to DoAny--which I did consider editing, clarifying and correcting in some respects. But perhaps here I can put the immediate question at hand more directly (the emphasis ...
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1answer
90 views

Can this previously solved three-dimensional constrained integration also be solved with certain added products in the integrand?

In Solved3DConstrainedIntegration the constrained three-dimensional (Hilbert-Schmidt-metric-based HSmetric) integration problem for the absolute separability probability of the two-qubit (quantum bit)...
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1answer
70 views

Counting Technique [closed]

Words with 6 letters are to be formed from the word "MEDICALOUS". If repetition is allowed, find the number of possible 6-letter words that can be formed if there is at least one letter ...
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4answers
565 views

Constant Distribution

As far as I know, Mathematica lacks a definition for a probability distribution representing a constant random variable. Is this assertion correct? Is there a problem in making such a distribution ...
5
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1answer
97 views

BoxWhiskerChart with summary statistics [duplicate]

I would like to duplicate a BoxWhiskerChart, such as this: but I do not have access to the full dataset that generated it. I'm happy to type in by hand summary statistics (such as mean, 25%, 75%, ...
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2answers
241 views

Optimizing sequential computation

The following question came up in reading group discussion of paper -- imagine taking two vectors, multiplying each by a random matrix, then taking tanh pointwise. If you repeat this process forever, ...
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3answers
213 views

Do any of the Mathematica CopulaDistributions (or others) fit well this sampled bivariate copula with uniform marginals over [0,1]?

I'm currently developing a data set that consists of two $50 \times 50$ matrices, which I designate as q1 and Q1. I strongly believe (bordering on formal proof [cf. Corollary 1 in marginalinvariance]) ...
3
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1answer
418 views

Use Kalman filter to predict

Here is a set of altitude data I collected with an Arduino sensor BMP-180 on a board CanSat data = {13.15, 13.4, 13.15, 13.31, 13.4, 13.31, 13.15,.....} how can ...
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2answers
324 views

How to explain `False == x && True == x`

Execute the following code: ...
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1answer
57 views

Probit with Equality Constraint

I have a set of data that I analyze using a probit model. However, because of the way that the data are produced, the effect of two variables should be equal. Say, it is a room tilting down from the ...
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0answers
34 views

Creating a distribution of random sample means

The following is taken from Chapter 19: Distribution of Random Sample Means from the book: Illuminating Statistical Analysis Using Scenarios and Simulations. Fifty random monkeys, each randomly pick ...
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2answers
197 views

CDF of experimental data

Here is data.csv: ...
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0answers
26 views

Building and Plotting a discrete CDF

I'm trying to plot the CDF of a simple "nCr" experiment: A box contains 4 screws and 6 nails. Two items are drawn at random without replacement. Let X be the number of nails drawn. I built a ...
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2answers
301 views

Polynomial fitting to obtain the growth rate

We -- my friend -- had asked a question here, which was not completely related to Mathematica, however, in a hope that someone familiar with the topic could help. There are still some aspects which we ...
2
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1answer
68 views

Convolution of two independent geometric random variables with parameters $p$ and $q$ [closed]

I am trying to use Mathematica to do some computations in Advanced Probability. I am quite new to Mathematica, so I need help in understanding the Convolve function. I used Mathematica 11 to compute ...
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1answer
58 views
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1answer
810 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
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1answer
193 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 ...
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0answers
28 views

How to draw a line marking where each chapter occurs in a text? [duplicate]

I am performing a text analysis on C.S. Lewis's book The Lion, the Witch, and the Wardrobe. I have created the following analysis of textual occurences of Aslan or Lion, Peter, Lucy, Edmund, Susan, ...
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1answer
76 views

Root mean square error of bearings

I have two sets of bearing angle data, one is forecast and the other one is actual, i.e. ...
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2answers
308 views

How can I speed up RandomVariate in the following case?

I would like to generate random values of some parameter with the weight being the Poisson distribution. An important point is that each time I generate the random number I need to consider the ...
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0answers
67 views

Full Information Maximum Likelihood - Under some other name in Mathematica

I have recently stumbled upon something called FIML - Full Information Maximum Likelihood. Apparently this methodology helps overcome missing variables provided the gaps are random. Searching the ...
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2answers
106 views

How to obtain the variance of a chi-squared distribution with Mathematica

I'm new to Mathematica and would like to show that for $x_1, ..., x_k$ independent, standard normal random variables the variance of the sum of their squares, i.e., $var(\sum_{i=1}^kx_k^2)$, is equal ...
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1answer
80 views

Evaluate area of random region covered by disks

If I cover a square of side $L$ with $n$ unit disks at random (the disks may overlap the boundary), is there a standard way to evaluate the total covered area $A$? I am looking to observe the density $...
3
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2answers
118 views

Specifying options to underlying `Integrate` when using `NExpectation`

I'm computing the max over a set of uniformly distributed random variables. I know that this value converges to 1 as the number of variables increases. Mathematica is having difficulty computing the ...
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2answers
44 views

`KernelMixtureDistribution` error message about precision

I want to use KernelMixtureDistribution to deal with a large amount of data points. For example, the following codes shows how I use it: ...
2
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1answer
51 views

Finding distribution of sum of two dependent variables

I am trying to find the distribution of the sum of two random variables $(x_1,x_2)$ which have the following distribution: $$f(x_1,x_2) = \begin{cases}2 ( x_1 + x_2) & 0 \le x_1 \le x_2 \le 1 \\ 0 ...
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1answer
78 views
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2answers
85 views

3D plot of the spatial path of velocity/space stochastic differential equations

I define the following 6 dimensional stochastic (Ito) process- in velocity v/position x. I can plot x1 as a function of t- see script below which has been corrected by Daniel. My goal is however to ...
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0answers
34 views

Unexpected behavior in Bootstrap confidence interval in Mathematica [closed]

EDIT: I think this is expected. There was a bug in my python code I'm computing a bootstrap confidence interval using Mathematica. ...
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0answers
76 views

Incorrect result of PDF

The execution of the command ...
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1answer
107 views

What is the probability that there are three or more consecutive numbers in these six cards?

52 poker cards (except the red and black jokers), 6 cards are drawn from them. What is the probability that there are three or more consecutive numbers in these six cards? The problem have been solved ...
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1answer
274 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 <...
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1answer
108 views

Solve for p of Binomial distribution

Is there a way to solve for the probability p of a binomial distribution in a set of equations? With some arbitrary functions g[ _ ] and f[ _ ] such that: ...
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2answers
707 views

Select rows of data that satisfies both conditions simultaneously

I'm a new user of Mathematica and now I am confused by a problem. Now I have about 2 million rows of data and 3 columns, i.e. a 2million*3 table. What I am trying to do is select rows of data ...
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1answer
66 views

How to add weights in fitting?

I have a set of data as: data = {{0, 0.046}, {40, 0.111}, {80, 0.291}, {120, 0.808}, {160, 1.742}, {200, 3.319}, {240, 5.017}, {280, 5.503}, {320, 5.897}} With ...
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0answers
31 views

How to compute the unbiased fit variance considering the option "Weights" in "NonlinearModelFit"

I am doing a non linear model fit. I know how the fit variance is computed when I do NOT assign weights to the fit, for example: ...
42
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1answer
2k views

How to fit a linear model in the Bayesian way in Mathematica?

Basically, I'm looking for the Bayesian equivalent of LinearModelFit. As of the moment of writing, Mathematica has no real (documented) built-in functionality for ...
3
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1answer
86 views

How does Mathematica compute the covariance matrix using "MultiNonlinearModelFit"?

I am doing a simple multi-non linear fit. I get the covariance matrix. Does anyone know how Mathematica calculate this Matrix? I have found the computation when mathematica fit only one signal but ...
5
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1answer
246 views

How to make this Box Plot

I want to mimic the following style (not necessarily the same data) So far, I got the following ...

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