Questions on the statistical functions of Mathematica.

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3
votes
1answer
91 views

Expectation problem using empirical distribution

I am having trouble with this Mathematica command: ...
-1
votes
2answers
188 views

Fitting a beta distribution to a probability density curve

If I have a spectral data set showing measured energy on the y-axis and frequency on the x-axis, how would I go about fitting this to a beta distribution? For example, lets say I had the data for the ...
7
votes
1answer
174 views

Mathematica Reference Book on Reliability Engineering?

Can anyone suggest a reference book titled “Reliability Engineering Using Mathematica” or similar that contains the version 9 or version 10 functionality ? Some topics/chapters I would be interested ...
2
votes
5answers
268 views

Generating a list of integers that roughly satisfy a distribution

Say I have a normal distribution, NormalDistribution[25, 7] I'd like integers from 1 to 50, not sampled at random from that distribution, but sampled in a way ...
10
votes
2answers
202 views

Probability of the sum of the largest n samples

15 numbers are randomly chosen from U(0,1), what is the probability that the sum of largest four numbers is greater than 3.5? ...
6
votes
3answers
138 views

Expected sum of largest 3

I pick 4 numbers from the Uniform Distribution. I need the expected value of the sum of the 3 largest. I am pretty sure that the answer is 9 / 5 which agrees with a simulation. I would like to get ...
8
votes
1answer
246 views

How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
4
votes
1answer
113 views

How to get an equivalent of WeightedData in Mathematica 8?

Is there an equivalent command of WeightedData (new in version 9) in Mathematica 8 or I have to define it by myself? I haven't found anything in the site or ...
2
votes
0answers
101 views

Where can I find the Distributions Palette?

I was watching the "Statistics: Modeling with Statistical Distribution" Training Course http://www.wolfram.com/training/videos/DAT016/ and in one of the slides, the following image showed up. Does ...
3
votes
0answers
220 views

What exactly is “ParameterErrors” of NonlinearModelFit?

I am trying to get what I call a "$\chi^2$ fit". This means taking a function $f(x,p)$ of the variable $x$ with a parameter $p$ and finding the value of $p$ that minimizes the "distance" from a data ...
0
votes
1answer
163 views

plot an exponential statistical function

I have this exponential function, where j is unknown. How can I plot the variance function for $k= 0.1, \; 1, \;10$ $$f_{j,k}(y)=\frac{\sqrt{j}}{\sqrt{2 \pi}}e^{\sqrt{jk}}y^{-\frac{1}{2}} ...
0
votes
1answer
189 views

How do I select a random sample without replacement? [closed]

What is the module that selects a random sample of size k (without replacement) from a given population of size n, involving the command Subsets.
3
votes
1answer
121 views

I need a technique for determining and drawing a line where the density in a listplot jumps up suddenly

Basically I have a two dimensional list plot with a bunch of points between the square of (0,0) and (1,1). The y-values of these points are drawn from a uniform probability distribution between 0 and ...
0
votes
3answers
325 views

Plotting confidence intervals

The documentation for PDF has an example for plotting a confidence interval of a standard normal distribution: ...
3
votes
1answer
133 views

Calculate the covariance of a large matrix

I have to compute the covariance of 50 very large integer matrices (2500x2000 elements). However, according to my estimation this will take around 10 days. Do you have any ideas how to speed things ...
7
votes
1answer
330 views

How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
2
votes
2answers
42 views

Evaluating a SmoothKernelDistribution at a point

I would like to evaluate the value of the following SmoothKernelDistribution at the location, say, 2.35. What is the right way to do it? ...
5
votes
1answer
147 views

Reverse engineer a sample value from a CDF

The image below shows the cumulative distribution of a normal distribution with mean = 4 and standard deviation = 1. Notice that if you have a value with a rank of 0.8 (meaning it would be 80th item ...
3
votes
1answer
145 views

How could I improve this Central Limit Theorem demonstration speed- and content-wise?

My purpose is to demonstrate the Central Limit theorem by assuming two custom distributions, taking some random samples, calculating their means and ploting the results. Ideally, the histograms should ...
11
votes
3answers
194 views

How to efficiently find moments of a multinormal distribution?

I have a multinormal distribution with covariance matrix $\sigma$ and zero mean. I want to find moment $$ E[x_1^{r_1}x_2^{r_2}\cdots x_n^{r_n}] =\,? $$ Of course, there is a build-in function ...
0
votes
1answer
115 views

Understanding distribution chart

How to explain DistributionChart function in mathematica, For example: if I have ...
3
votes
2answers
285 views

KolmogorovSmirnovTest[] On Frequency Data

I have two observed frequency data, let say f1 = {100, 200, 150, 100, 50}; f2 = {110, 195, 160, 105, 40}; and i want to know whether these random samples belong ...
2
votes
1answer
162 views

Judging the quality of fitting an EventData object to a distribution using LogRankTest

I have $389$ data points defined in an EventData object and want to judge the quality of fit of this data to a fitted $3$-parameter Weibull distribution. This ...
-3
votes
3answers
179 views

Statistical analysis of a data file and its Plot [closed]

As the title says, I have an external data file which contains thousands lines of data. The data file contains eight columns and here is what I would like to plot: Let's assume that the length of the ...
4
votes
1answer
434 views

How does Mathematica estimate error on fit parameters?

When performing a fit using NonlinearModelFit (or any of Mathematica fitting functions, but I am particularly interested in nonlinear models), Mathematica makes a ...
0
votes
0answers
124 views

Discrete distribution binomial set up

I hope one of you guys can help me out. I am trying to visualize a discrete distribution based on a binomial distribution and a mixed binomial distribution. In the first step I started to determine ...
5
votes
1answer
109 views

PearsonChiSquareTest: set degrees of freedom

How to set degrees of freedom for PearsonChiSquareTest? I have this: ...
3
votes
3answers
375 views

Log-log scale smooth histogram

How can I create a smooth histogram with a log-log scale? I can use Histogram[data, "Log", "LogCount"] to get a log-log histogram, or I can use ...
3
votes
3answers
220 views

How to partition a list into sublists in a similar way to Histogram

I have a list of list as below (I show part of it) ...
3
votes
1answer
125 views

How to Use ProbabilityScalePlot with Censored Data?

I am trying to reproduce a ProbabilityScalePlot of censored data shown here (see Sample Analysis Plot). Here is my Mathematica code. First I deal with the uncensored case. ...
6
votes
1answer
497 views

How do I calculate Standard Deviation confidence intervals in Mathematica?

I have a series of simulation results and I would like to demonstrate how the confidence interval for the mean and standard deviation decrease as the number of results increases. I have done this for ...
4
votes
1answer
160 views

Defining five-parameter Pearson distribution by moments

How do you derive (or where can I find a derivation of) the equations to match the five parameters of a general Pearson distribution to a mean, variance, skewness, kurtosis, and condition that the ...
5
votes
1answer
613 views

Hodrick–Prescott filter (one-sided version)

I am interested in implementing Hodrick–Prescott filter (HP filter) on my time series data in Mathematica. I know that there is already a version of two-sided original filter for Mathematica (see ...
2
votes
2answers
231 views

SinglePredictionBands versus MeanPredictionBands from NonlinearModelFit

From my Statistics lectures I know the term confidence and prediction interval, whereas the confidence interval is smaller than the prediction interval. If I plot the mean and single prediction bands ...
2
votes
1answer
95 views

Confidence level for Binomial

For 617519 first time births there were 317528 boys. Give an estimate with 99% confidence interval for the probability that the first time birth is a boy. I have searched for the confidence ...
1
vote
1answer
128 views

Value for x such that |(x-y)| is minimum

I have a list Y={y1,y2,y3,...,yn} And I would need to find x such that Abs[x-Y[[i]]] for all $y_i$ in $Y$ is minimum. ...
6
votes
3answers
422 views

Calculate probability function

I would like to calculate the following with Mathematica: Let $X$ be a random variable with probability function $$p(x)= \left\{ \begin{matrix} \frac{x}{6} & \text{for }x \in \{1,2,3\}\\ 0 ...
12
votes
1answer
227 views

Randomness test suites that can be invoked from Mathematica

There are several test suites referenced at csrc.nist.gov designed to test a (pseudo-)random byte sequence for randomness, and discover possible skews, correlations, patterns, or other hidden ...
4
votes
2answers
319 views

How to make a conditioning plot?

I'd like to make a conditioning plot just like coplot in R. Is there a pre-made solution or do I have to make a bunch of plots individually? Edit: This is an example from r screenshots. It is a way ...
0
votes
1answer
476 views

PDF of binomial distribution and mixed binomial distribution

I want to plot the PDF of binomial distributed function and a mixed binomial distributed function, therefore I entered for the binomial distribution function the following: ...
1
vote
0answers
547 views

How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
0
votes
1answer
139 views

plot probability

Hi I just want to flatten a function, I tied it with Joined->True, but it did not work, hope somebody of you can help me. This is my code: ...
2
votes
1answer
240 views

Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
2
votes
0answers
45 views

How can I account for assumed X and Y errors when using findfit? [duplicate]

I'm using very noisy biological data, and I need to assume, when doing linear regression, that there are errors in both X and Y. ...
3
votes
1answer
161 views

DistributionFitTest with WeightedData?

My problem is related to statistical testing with weighted data. I have a data sample and I assume that a part of the data follows a specific distribution (Pareto). So I fit my data to a distribution ...
0
votes
0answers
98 views

Binomial Distribution (binomial model inspired by Merton)

Binomial Distribution (binomial model inspired by Merton) Hi I want to do the following and I hope that anyone of you can help me out. In short, I have a portfolio consisting of 10 companies, ...
0
votes
1answer
109 views

Distance to a MultivariateStatistics median

I have a population of objects (each of which is described by a list of about a half-dozen real numbers), and I'd like to find some reasonable kind of distance between each of several different test ...
0
votes
2answers
577 views

How to generate a random data set with determined expected value and variance? [closed]

Recently I am doing my math homework and there is a question asking me to Come up with a dataset X that has at least 10 distinct numbers in it such that Expect[X] = 3.7, and Var[X] = 2.1. Actually I ...
4
votes
2answers
253 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
1
vote
0answers
161 views

Simulations with MonteCarlo and Autoregressive methods

I am trying to find the best-fit trend for my data. Here I just generated it but let's say I don't know my data trend at all. ...