# Tagged Questions

Questions on the statistical functions of Mathematica.

236 views

### 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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### on Kolmogorov-Smirnov test

I found a problem to calculate Kolmogorov-Smirnov test statistic or p-value the data is ...
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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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### 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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### 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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### Estimation of vector autoregressive (VAR) process

To estimate 1-dimensional VAR process (which is AR process) you can easily use functions EstimatedProcess or ...
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### Obtaining joint distributions and conditional distributions using Mathematica

I have two multivariate Gaussian distributions $p(x)$ and $p(z)$ with mean vectors $m_x$ and $m_z$, and covariance matrices $\Sigma_x$ and $\Sigma_z$. my model is a simple linear model $x = W z+n$ ...
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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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### Plotting a frequency function

I have a list of numbers and I want to plot the fraction of numbers >= k against k which will naturally be a decreasing curve. How do I do that?
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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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### 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 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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### 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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### 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 ...
The following evaluation fails (the result is just the copy of the input) $$\text{Probability}[0<x\leq a | x-y=t,\{x\ {ExponentialDistribution}[\lambda ],y\ {ExponentialDistribution}[\lambda ... 1answer 648 views ### PDF of binomial distribution and mixed binomial distribution I want to plot the PDF of binomial distributed function and a mixed binomial distributed function, therefore I entered for the binomial distribution function the following: ... 0answers 111 views ### How to include confidence intervals into ProbabilityScalePlot? I use ProbabilityScalePlot[data, "Weibull"] to plot measured data and ... 1answer 175 views ### Calculate the covariance of a large matrix I have to compute the covariance of 50 very large integer matrices (2500x2000 elements). However, according to my estimation this will take around 10 days. Do you have any ideas how to speed things ... 1answer 60 views ### TransformedDistribution with respect to new variable Given a custom pdf f_x(x), I'm trying to find it's transformation f_y(y) where$$y=x^2$$and$$f_x(x)=30*x^2 (1 - x)^2, 0<x<1$$I tried to using the following commands: ... 0answers 60 views ### k-means clustering using squared correlation in Mathematica I am trying to cluster data using the squared correlation coefficient since in the case of my data, -1 correlation is equivalent to 1 correlation (polarities do not matter). How can this be done in ... 1answer 124 views ### Statistics confusion I have two data sets. When I do a QuantilePlot[data1, data2], I get the graph below. However, ... 1answer 144 views ### How to use a custom CDF in a Kolmogorov-Smirnov test How do I use a custom CDF that I defined for a Kolmogorov-Smirnov test. I have one input vector of data whose CDF I claim to have derived but want to check whether it agrees with my closed form ... 2answers 83 views ### Behavior of Commonest when there is an even split between the elements of the list it is given How can I alter Commonest so that, when I give it an input of four zeroes and ones such as \{0,1,1,0\}, which has an even split in its elements, it returns the ... 0answers 136 views ### Is this the correct method in using bootstrapping to determine a lower confidence bound? Quite often in industry, due to cost and schedule constraints, decisions must be made on small sample size data. I have 4 cycles-to-failure values resulting from running samples to failure in a ... 3answers 631 views ### Creating word histograms from lists of strings Consider the following: ... 1answer 76 views ### Stochastic Approximation and Simulation using Running Median I have a function$$F(X_{t+1},Y_{t}^{med})= \alpha X_{t+1} + (1-\alpha) Y_{t}^{med},$$where$$Y_{t}^{med} = Median(Y_1, Y_2,... Y_t).$$Moreover, Y_1 = X_1 and Y_t = F(X_{t},Y_{t-1}^{med}) ... 3answers 376 views ### Creating Correlation Table (and Working) With Missing Data I am working with data that contains missing values (I have several variables (across the columns) and several observations (across the rows) in an excel spreadsheet). Example of the data structure: ... 1answer 192 views ### Simulation Sample Paths for Stochastic Approximation Algorithm Let X_t be IID random variables in [0,1] and CDF F(\cdot). Suppose there exists a variable Y_t given by: Y_1 = X_1 and Y_t = \phi(X_t, \overline{Y}_{t-1}), \forall t >1, where ... 3answers 150 views ### Expected sum of largest 3 I pick 4 numbers from the Uniform Distribution. I need the expected value of the sum of the 3 largest. I am pretty sure that the answer is 9 / 5 which agrees with a simulation. I would like to get ... 2answers 417 views ### SinglePredictionBands versus MeanPredictionBands from NonlinearModelFit From my Statistics lectures I know the term confidence and prediction interval, whereas the confidence interval is smaller than the prediction interval. If I plot the mean and single prediction bands ... 1answer 143 views ### Simulation Beta Distribution Suppose a function such as: \phi^{\alpha} (x,y) = \left\{ \begin{array}{l l} \alpha x & \quad \text{if x < y}\\ x & \quad \text{if x = y}\\ \alpha x + (1 -\alpha) & ... 2answers 237 views ### build and estimate a time series process I want to generate an EGARCH process. My problem is that I do not see how to create new processes beyond those available. The process itself is :$$\epsilon(t) = \sigma(t) \eta(t)$$... 1answer 82 views ### 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 ... 1answer 65 views ### Can I use boolean parameters in LogitModelFit? For example, to use 1 as True and 0 as False: ... 4answers 325 views ### Conditional Expectation — How can Mathematica find a more general closed form? Mathematica can't find a solution to this Expectation. ... 1answer 87 views ### 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. ... 0answers 69 views ### 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. ... 3answers 2k views ### Histograms with pre-counted data I've got some large data sets which have been counted but not binned already - essentially, a list of pairs of values (not bins) and counts.* (Or, equivalently, it's been binned into too-small bins.) ... 1answer 411 views ### Fitting data to a Poisson distribution I'm trying to fit a Poisson Distribution to data produced in a lab. I've successfully made a Histogram of the data, which looks like: However, when I try to fit the Poisson Distribution using: ... 2answers 339 views ### Finding Expectation of function of a Log-normal distribution Say Y=g(X) and p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma } is Log-normal density function: [Wiki] Find E[Y]? Since E[Y] = \int_0^\infty y f_Y \ dy = ... 2answers 351 views ### Error function fit of data I have this experimental data set which I know should follow the Complementary error function. My goal is to find the σ of the associated gaussian distribution. However, I cannot seem to do it in ... 2answers 219 views ### Measures of association, Concordant and Discordant I want to calculate concordant and discordant pairs on nx2 tables. ... 2answers 424 views ### Visualization: elliptical insights into data sets… I was recently reading the following paper on visualization techniques using ellipses to gain statistical insights. Elliptical visualization for looking at correlations has briefly been touched on ... 1answer 299 views ### Generating a list of standard normal random variables Im trying to generate a list of random (standard) independent normal variables. For this, I first generate a random list of, say, 100 real numbers in the range [0, 1000], and then make them standard ... 1answer 193 views ### Moment central of a binary image I am implementing the Hu set of invariant moments detailed here Hu set of invariant moments. I implemented the moment Image like this: ... 2answers 282 views ### On Parameter Estimation using FindDistributionParameters I am a novice of Mathematica and have recently started my self-study of maximum likelihood estimation (MLE) using Mathematica. I would like to estimate the parameters associated with a distribution ... 1answer 779 views ### Is there a free version of the Springer book “Mathematical Statistics with Mathematica”? Is there a free version of the Springer book:$$\text{Mathematical Statistics with Mathematica} by Rose and Smith ... available on the internet?
I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & \$E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...