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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0
votes
0answers
59 views

Need to plot binomial distribution probabilty function [on hold]

I am incredibly new to using Mathematica, and struggling to learn it as I have very little experience with any sort of software more complicated than excel, so I am very sorry if this is a stupid ...
3
votes
4answers
137 views

Calculating expected value from paired values and weights

I'm very new to Mathematica. I just need a quick solution on how to multiply x with y when a data set is given as ...
3
votes
3answers
150 views

How to Plot the PDF of Product of two Normals

I've been looking to plot the distribution of the product of two normally distributed variables, x and y, that are uncorrelated. I've tried symbolically calculating the PDF using the ...
0
votes
1answer
44 views

Changing notations for probability moments with subscripts

Suppose I have have two kinds of variables $X_{\alpha_j}, X_{\beta_k}$ in the form of Subscript[x,Subscript[α,j]] and ...
4
votes
1answer
100 views

Why doesn't NSolve work for this equality? Wildly incorrect solutions are given in certain cases

I am trying to write a function that solves for p in the following equation: PDF[BinomialDistribution[n, p], x] == op The ...
10
votes
1answer
80 views

FullSimplify on TransformedDistribution

Bug introduced in 8.0.0 Could someone check that I haven't gone mad? I would like to take the maximum of two $[0, 2 \pi]$ independent uniform random variables. ...
13
votes
3answers
152 views
0
votes
2answers
46 views

Custom multivariate discrete distribution [closed]

This is related to How to define an n-variate empirical distribution function probability for any n? and RandomVariate from 2-dimensional probability distribution but I don't think neither questions ...
2
votes
3answers
98 views

slwcon and eincr in integrating multivariate Gaussian random variables

Why is the following integration involving multivariate Gaussian distribution so slow and generating an error? Is there a better integration strategy? All that I'm doing is considering ...
1
vote
1answer
28 views

Histogram and Random Lists [closed]

Suppose I have the following list listrand of random numbers from RandomReal[-30,30] (where the size of the list is 40). Is ...
4
votes
0answers
94 views

Goodness of Fit of Copula Distribution

I am trying to find out goodness of fit of copula distribution, but Mathematica 10 gives me the same answer for each copula type. e.g ...
2
votes
1answer
58 views

Efficient way to apply linear function to multivariate polynomial [closed]

Suppose I start with an expression that is a multivariate polynomial in $x_k$'s, $$W = a + b \cdot x_1^{n_1} x_2^{n_2} x_3^{n_3} x_4^{n_4} + c \cdot x_1^{m_1} x_2^{m_2} x_3^{m_3} x_4^{m_4}$$ where ...
0
votes
0answers
36 views

Detect abnormal values [migrated]

Suppose that we have a monotonic sequence, and one of the values in this sequence is abnormal (it can be less or higher than the "true" value). How can we detect it? Could you suggest a good ...
2
votes
1answer
85 views

Defining symbolic expectation function

I want to define the standard expectation $E$ operator in Mathematica. In particular, I want it to satisfy, $E[ c + a \cdot X_1^{n_1} X_2^{n_2} X_3^{n_3} X_4^{n_4} + b \cdot Y_1^{m_1} Y_2^{m_2} ...
1
vote
1answer
58 views

Defining Probability Distribution with parameters

I have a family of probability distributions, indexed by elements in $\mathcal I =\mathbb N \times [0,1] \times [0,1]$. For each $(A,B,C) \in \mathcal I$ I know how to define the corresponding ...
4
votes
1answer
120 views

How to transform an image into a probability density function?

I'd like to use the Metropolis algorithm to randomly generate points with density according to the brightness of an image. I just need to transform a binary image into a pdf function to use this ...
-2
votes
0answers
33 views

histogram of imported data shows a single bin

I have timing data imported as CSV: ...
20
votes
2answers
531 views

Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?

So, given some data, Mathematica 10.2 can now attempt to figure out what probability distribution might have produced it. Cool! But suppose that, instead of having data, we have something that is in ...
10
votes
2answers
125 views
3
votes
1answer
173 views

Using Probability for n-gram string queries

I want to use Probability to ask questions on strings like "what's the probability of the occurrence of the trigram 'the' conditioned on the occurence of the digram 'th'?" This doesn't work. I ...
5
votes
1answer
123 views

How are p-values in fittings estimated?

I am trying to understand how p-values retrieved in a ParameterTable estimated but I couldn't find any specific information in the documentation about this. For instance, considering ...
4
votes
0answers
57 views

How to define a bivariate skew normal distribution?

There is BinormalDistribution that handles easily bivariate normal distribution and its mixtures. There is also ...
1
vote
0answers
39 views

Mixture of a bivariate distribution defined as a copula

I define a bivariate distribution: ...
5
votes
1answer
77 views

Integrate yielding a ConditionalExpression but I don't think the condition is necessary

Suppose I take the PDF of the LogNormal distribution with parameters m and s evaluated at x. I obviously get an expression involving m. I now want to integrate that expression not with respect to x ...
0
votes
1answer
58 views

kernel density estimation

I am trying to compute CDF of historical data ( weekly change in CDS spread) using kernel density estimation. The original data has 300 observation. I uploaded data from excel ...
1
vote
0answers
42 views

Reducing quantile & color map queries for use with Associations

This set of queries perform basic maps to quantile and then color-map. There's got to be a more compact solution. What are some approaches to reduction? Numeric: ...
2
votes
1answer
45 views

Documentation for the Bounded option of SmoothKernelDistribution

I have found the Bounded option useful in the SmoothKernelDistribution function, but I can't find any documentation for exactly ...
0
votes
0answers
80 views

Nasty nested Integrals

I would like to solve following integrals by Mathematica ...
1
vote
0answers
39 views

How does Matematica compute the CDF of the binomial distribution?

I want to know, how Mathematica actually implements the cumulative distribution function of the binomial distribution. Which algorithm does Mathematica use to compute ...
5
votes
2answers
130 views

How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
2
votes
3answers
185 views

Fitting and plotting Weibull distribution

How can I find the best fitted 2-parameter Weibull's distribution (PDF) to describe my data? How can i plot my data and estimated distribution all in one graph? How can I show/compare results of ...
17
votes
4answers
1k views

Using Mathematica to solve a probability problem

The problem is from Principles of Statistics by M.G. Bulmer: In a certain survey of the work of chemical research workers, it was found, on the basis of extensive data, that on average each man ...
0
votes
1answer
86 views

Creating a residual histogram from discrete 3D data and function [closed]

Hi I have this data and my function on Mathematica: ...
5
votes
2answers
98 views

Dirichlet marginals - why does Mathematica not give the *Kth* marginal?

Observe: MarginalDistribution[DirichletDistribution[{a, b, c, d}], #] & /@ Range@4 {BetaDistribution[a, b + c + d], BetaDistribution[b, a + c + d], ...
-1
votes
2answers
96 views

Using Mathematica to calculate expected time to absorption [closed]

I am trying to solve a standard ETA on a birth-death process with $n$ states $\in \{0,\cdots,n-1\}$ where state $n-1$ is absorbing. Also $\mu_i$ is the expected time to absorption starting at state ...
2
votes
1answer
66 views

How do I define a random variable involving Part?

I need to define a random variable that involves Part, but when I try, for example ...
0
votes
0answers
41 views

R^2 values for piecewise regression

So I've used NonlinearModelFit on a Piecewise function and gotten a nice little piecewise regression. This is what my code looks like: ...
9
votes
1answer
201 views
1
vote
1answer
76 views

Is there any way to perform an ANOVA test given $n$, $\bar{x}$ and $S^2$?

Suppose I have the following data about the incomes of residents of three cities. $$ \begin{array}{|l|c|c|c|} \hline & n & \bar{x} & S^2 \\ \hline \text{City A} & 10 & 2.8 & ...
2
votes
1answer
118 views

trajectory density plot

I want to make a plot that shows the density of trajectories (x-y plots). In other words I want a plot that's analogous to this but with curves instead of points as data. Here's what I'm doing ...
8
votes
2answers
216 views

FWHM of an image

What is a resourceful method to calculate FWHM (full width at half the max) of every column in an image. Assuming the image is having a very high resolution for example 1944 x 2592. Logic so far ...
2
votes
0answers
40 views

Covariance matrix estimation when number of variables is larger than number of observations

It is well known that the sample covariance matrix estimator results in a singular matrix if the variables is larger than the number of observations. One solution is to apply shrinkage estimators. ...
25
votes
0answers
383 views

Summer Solstice Spurious Correlations Challenge

I came across this hilarious web site that has charts of bizarre "correlations" between disparate categories. Results like this: In the spirit of my summer solstice shedding spuriously earned rep. ...
3
votes
2answers
86 views

Efficient Sampling of A (Countable) Discrete Distribution

I have a sequence of positive terms $(a_n)$, for which $\sum_{n=1}^\infty a_n = A <\infty$, and wish to take a psuedo-random sample from the discrete probability distribution \begin{equation} ...
2
votes
1answer
90 views

P-Values are inconsistent when using DistributionFitTest repeatedly

I am attempting to become more familiar with the DistributionFitTest, specifically the distributions it yields and their fittedness. What I have found is that when I generate random data, fit it, and ...