# Tagged Questions

Questions on the statistical functions of Mathematica.

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### Binomial Regression where n > 1

I am not well versed in Generalized Linear Models, but am trying to use this approach to model some discrete data. I have binomial data where the sample size for each observation is the same size, ...
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### Robust (White) estimation with LinearModelFit?

You can make a robust estimate (White) by LinearModelFit or GeneralizedLinearModelFit? Thanks.
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### Mixture / Hierarchical Distribution from Conditional

How does Mathematica handle Hierarchical distributions. For example, if I have X|Y ~ Poisson(Z) Y ~ Exp(lambda) Z ~ Normal(0,1) First, of all, the distribution of X is only given conditionally and ...
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### probability calculation with two independent normal RVs

I don't understand why Probability[X < Y, {X \[Distributed] NormalDistribution[0, 1], Y \[Distributed] NormalDistribution[0, 1]}] gives 1/2 while we know ...
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### Method of moments using just the moments?

FindDistributionParameters (and EstimatedDistribution) can use "MethodOfMoments" as its ...
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### The CorrelationMatrix is equal to corrcoef of Matlab?

I know that my question imply to know matlab, and this is not the right place, but i'm a physics student and i don't quite yet understand this concepts. When i make a LinearModelFit i can get a ...
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### Find a probability with random variates from the same distribution

I'm trying to find Probability involving 3 random variates from the same distribution, but Mathematica does not seem to solve it. ...
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### Central Limit Theorem - solve for a const, given probability

I hope this is not a very complicated question, but I have problems finding the answer. Quite often, I need to calculate something like this: $P(-a<\bar{x}<a) = p$, where $\bar{x}$ refers to the ...
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### How to group box-and-whisker in parallel for comparison in BoxWhiskerChart?

I have two collections of data: xdata and ydata ...
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### plot the numerical value of the average on a BoxWhiskerChart

Im using BoxWhiskerChart to get a boxplot of a matrix of two columns. I need to read the value of the sample average directly from the plot and not from the axes. ...
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### How can I best plot timestamps by frequency-to-date?

I have a site called Sudomemo. I record when I first see a user in the database; and I've exported it in JSON format, located here. http://www.sudomemo.net/statistics/firstSeenDump.php I've done ...
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### what is The Formula behind the Kolmogorov-Smirnov test statistics?

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
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### How do I display the plane of best fit in 3D?

I'm trying to display the plane of best fit in the same 3D-box. Currently, I have the following code which spits out a plot of the points in 3D. I want to have a plane of best fit, can Mathematica do ...
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### Comparing heavy tailed and non-heavy tailed distribution using Mathematica

I have data from a heavy tailed distribution (see picture 1) and a non-heavy tailed distribution (see picture 2) and want to compare it using a histogram on log-scale. However the picture 3 does not ...
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### Distribution of block maxima of gaussian random variables

I try to verify the following result of extreme value statistics that the distribution of the block maxima of Gaussian random variables converges to a Gumbel distribution. To this end, I first ...
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### on Kolmogorov-Smirnov test

I found a problem to calculate Kolmogorov-Smirnov test statistic or p-value the data is ...
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### In there a way to derive the inverse value of CDF format MultinormalDistribution?

Is there a way to produce the inverse value of multinormal distribution function in CDF format with 0.05 significance level? I found the function called ...
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### Statistical Analyzis of Observed Data (Queuing Process)

Basically I have a process that belongs to a certain state at any point of time. However, the time intervals are not fixed (in fact they are exponentially distributed). Essentially, the data points ...
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### RandomFunction and Histograms

RandomFunction[QueueingProcess[3, 5], {0, 15}] Histogram[data, Automatic, "PDF"] gives a very nice way to see the histogram based on the specified process. ...
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### How to derive SinglePredictionBands from a NonlinearModelFit model

I have found NonlinearModelFit to be extremely useful in my work. Here I have fit 4 points to a function and am being asked to explain how the 95% SinglePredictionBands associated with the plot below ...
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### Getting the Cumulative Distribution Function of f(x) from a dataset of x

I've a data set $\mathcal{X}$ which consists of randomly generated numbers. Let's say for example data = RandomVariate[ExponentialDistribution[1], 10^4]; My aim ...
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### On plotting the Weibull distribution

First: How can I plot the Weibull distribution with parameters a = 2 and b = 3.5 on the range of ...
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### QuantilePlot silliness

When I do a quantile plot of two large data sets (in my case, each of them of size around 3 million), the resulting notebook cell is huge, and if you save it as PDF, the resulting PDF is 13MB in size. ...
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### Estimating Confidence Interval Variance covariance matrix from weibull distribution

In The following Example 50 obs . I estimated distribution parameters (by point) but *i want to estimate parameters by confidence interval and calculate covariance matrix i need help * ...
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### Choosing The Best Fitted Probability Distribution Model

The following Example 20 Obs and i used Goodness of fit test with Exponential distribution, another time with Weibull distribution and third time with Pareto distribution .All of them are significant ...
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### Estimating Parameters of a Custom Distribution

The problem is I can not get estimation of parameters of any custom probability distribution (distributions are not built in Mathematica), here is an example: First: I entered random numbers of ...
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### How to include confidence intervals into ProbabilityScalePlot?

I use ProbabilityScalePlot[data, "Weibull"] to plot measured data and ...
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### TransformedDistribution with respect to new variable

Given a custom pdf $f_x(x)$, I'm trying to find it's transformation $f_y(y)$ where $$y=x^2$$ and $$f_x(x)=30*x^2 (1 - x)^2, 0<x<1$$ I tried to using the following commands: ...
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### Meaning output ANOVA post hoc tests

I am carrying out an ANOVA in Mma, and I wanted to apply a post-hoc test, but I do not understand the output that is given. It says e.g. Model-> Duncan, {4, 5} ...
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### Creating Correlation Table (and Working) With Missing Data

I am working with data that contains missing values (I have several variables (across the columns) and several observations (across the rows) in an excel spreadsheet). Example of the data structure: ...
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### Simulation Sample Paths for Stochastic Approximation Algorithm

Let $X_t$ be IID random variables in $[0,1]$ and CDF $F(\cdot)$. Suppose there exists a variable $Y_t$ given by: $Y_1 = X_1$ and $Y_t = \phi(X_t, \overline{Y}_{t-1}), \forall t >1$, where ...
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### Truncated Distribution Parameter Search Produces Singular Jacobian Using FindRoot [closed]

I'm trying to find the 2 parameters of a truncated Weibull distribution using version 10 and FindRoot. I would like to truncate the distribution between t =0 and t = 3600 with the probability of ...
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### Median of Dataset in Mathematica 10

I'm having trouble calculating the median of a Dataset[] in Mathematica 10. The situation is as follows. Consider a dataset that was defined as follows: ...
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### Correlation test issues

No error in 10.0.2 When using Correlation[] function I sometimes get the strange warning: ...
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### Simulation Beta Distribution

Suppose a function such as: $\phi^{\alpha} (x,y) = \left\{ \begin{array}{l l} \alpha x & \quad \text{if$x < y$}\\ x & \quad \text{if$x = y\$}\\ \alpha x + (1 -\alpha) & ...
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### Solving minimum length confidence interval problem

I'm trying to find the minimum length of a confidence interval for the variance from a sample iid with normal distribution. I tried ...
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### Can I use boolean parameters in LogitModelFit?

For example, to use 1 as True and 0 as False: ...
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### Conditional Expectation — How can Mathematica find a more general closed form?

Mathematica can't find a solution to this Expectation. ...
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### ZTest result not making sense

I'm using version 10. I'm having difficulty with understanding why I'm getting some output from the ZTest function. Here is the code for my specific example. ...
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### Why do EstimatedDistribution and DistributionFitTest work this way

I am fitting some time-series data to both a stable distribution and a normal distribution in order to assess the goodness of fit of each. Along the way I encountered the following confusing result. ...