A distribution is a mathematical description of probabilities or frequencies.

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Johnson transformation in Minitab allows a too narrow data range

I am using Individual Distribution Identification in Minitab 16, to identify the distribution of 19 values. The Johnson transformation is the only decent fit, and the equation I get is the following: ...
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19 views

Convert probabilities of “binomial events” into beta distribution for binomial parameter (theta)

I have three events that essentially arise from a binomial distribution with k=2, i.e., X~Binomial(theta,n=2). Given some model and data I obtained a conditional (pos distribution for a particular ...
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9 views

Handling a censored factor score?

I have an 11 item measure for which I am computing factor scores. It is a censored (floor effect) measure. EFA/CFA analysis indicates I should remove 3 of those items. Whether or not I remove those ...
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67 views

The frequency in histograms

My question is trivial, but the problem is that I found contradictory answers on internet. So I have the following sample data: ...
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1answer
40 views

R - Same Density but different QQ-Plot?

I have data variable corresponding to quotation amount and I want to find which statistic law this variable follow if there is one. It seems that the ...
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12 views

Comparing normalized and partially normalized quadratic form of normal variables

Suppose $X=(X_1,X_2,\ldots,X_n)' \sim \mathcal{N}(0,\Omega)$, where $\Omega$ is the variance-covariance matrix of dimension $n\times n$ for the vector $X$. Let $a=X'\Omega^{-1}X$. It is known that ...
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1answer
31 views

What distribution has this non-central Chi-Squared -like moment generating function?

I'm new here so please criticize errors! My moment generating function looks like this (after some tidying): $E[e^{wY(t)}] = \frac{1}{\left(1-2\theta(t) w\right)^{k/2}} ...
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19 views

Sample from a quotient of mixture distributions

I want to sample from a random variable $Z=\frac{X}{Y}$, where $X$ and $Y$ are mixtures of distributions. I figured out, how to sample from a mixture distribution (e.g. Simulating random variables ...
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18 views

Role of Distribution , likelihood function, and MLE in regression ?

I'm currently a beginner in learning statistics. In regression part, we started to learn (software) using MLE method for estimating parameters in the models. In order to calculate MLE, likelihood ...
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5 views

Objective evaluation of subjective data points and normalization

I want to write an access database that takes in inputs from instructors ranking a student on their performance in a handful of categories. (1 - below average, 2 - average, 3 - above average). They ...
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1answer
63 views

Sum of two independent random variables (application: inter-arrival times)

In the case of specifying the requests' inter-arrival times of a web server. Let us suppose the following case: (imagine they came from an exponential random function) client1 a stream of $15$ ...
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2answers
52 views

Generating Beta distribution from Uniform distribution

I can generate as many samples from one or more uniform distribution (0,1) as I wish. How can I use this to generate a beta distribution ?
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27 views

Simulation & statistical distribution

Can you still use simulation techniques if you do not know about the statistical distribution of the population under study?
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33 views

Binomial Distribution With Scale Variable?

I'm attempting to generate some random data using a distribution. I need each random point to fall within a certain range e.g. 0-20, and I would also like to control where the center of the curve ...
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14 views

Relationship between Poisson arrival rate and Exponential inter-arrival rate

A poisson distribution has a lambda 1.5 per minute. I would like to know as to how would i use this for the lambda in exponential distribution? Would both the lambda values be the same?
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2answers
32 views

How close does a distribution have to be to normal, in order for predictions to be accurate?

I know a Kolmogorov-Smirnov test will tell me if a sample distribution belongs to a normal distribution or not, with a certain probability (correct me if I am wrong?). I performed a KS test on my ...
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1answer
356 views

Why is a “negative binomial” random variable called that?

I don't understand why the "negative binomial" random variable has that name. What is negative about it? What is binomial about it? What is negative-binomial about it?
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14 views

How to calculate distribution of (X1, X2) conditional on (C1, C2) in statistical model?

Say that $X_{1}$ = $a_{1}$$X_{2}$ + $B_{1}$$C_{1}$ + $E_{1}$ and $X_{2}$ = $a_{2}$$X_{1}$ + $B_{2}$$C_{2}$ + $E_{2}$ where $E_{1,2}$ are jointly distributed normal with 0 mean and variance ...
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6 views

Fitting a power law to existing integral

I have empirical data - people from cities - a certain number of people for a certain number of cities. I know the exact number of cities, as well as the exact number of total people - e.g. the ...
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1answer
134 views

Example of heavy-tailed distribution that is not long-tailed

From readings about heavy-, and long-tailed distributions, I understood that all long-tailed distributions are heavy-tailed, but not all heavy-tailed distributions are long-tailed. Could somebody ...
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2answers
33 views

How could calculate sampling size for 95% confidence in a unique distribution?

I made a big list of words that I claimed more than x% of them have dictation error. For showing my confidence of claim I need to show a sample(random) that prove it(because I can survey a sample list ...
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2answers
80 views

What is the difference between multimodal and multivariate?

Can somebody explains me the difference between "multimodal" and "multivariate"? For example, I have a dataset which contains different information. All information objects are connected together ...
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24 views

Can any distribution be fully described by the [infinite] set of all its moments? $\{E[x^n]\}_{n\in N}$ [duplicate]

Is it possible describe any distribution uniquely by the infinite set of all it's moments $\{E[x^n]\}_{n\in N}$ If yes, does that include discrete, truncated, etc. distributions? If not, is this ...
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65 views

Probability of a run of events from past data

I would like to calculate the probability that there will be a car crash at a certain crossroad for three days in a row. I would like to compute that based on the data I have about the crashes in the ...
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4answers
409 views

Example of distribution whose support is strictly positive

I am looking for something similar to the normal distribution in which there are a mean and a standard deviation representing the amount of variation. However, the value must always be positive, i.e. ...
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3answers
28 views

Correlation matrix disturbances (shocks)

I need ideas on generating disturbances of the correlation matrix. Say, I have a n-by-n correlation matrix $C_{i,j}$. I'd like to shock it, and produce the disturbed matrix $C'_{i,j}$ and see what ...
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17 views

What is the point of finding a representative sample distribution rather than calculating the probabilities directly from the sample?

The only advantage I can see is in using things like confidence intervals determined from the distribution, but I constantly see people fit a distribution to a sample and use that to calculate the ...
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23 views

Requirement on data distribution when using certain data mining classifiers

I am a little bit confused on whether data mining classifiers make any assumptions about the distribution of the data. I myself have a computer science background, but when I have discussions with an ...
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1answer
60 views

Probability of an unknown distribution

I have the sample of a variable $X$ whose distribution is unknown and I would like to know how to estimate the probability of $X$ taking some values. How can I do that? I assume that there's a non ...
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52 views

Distribution of geometric mean of normally distributed independent random variables [closed]

Suppose we have $X(i)$ for $i=1,...,n$ normally distributed independent random variables with the same known $\mu$ and $\sigma$ for all: $$X(i) \tilde{} N(\mu,\sigma)$$ Suppose that we take the ...
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5 views

link fx and distribution in GEE model

I am working on my dissertation using a GEE approach. The reason is that my outcome is nonnormal, nonlinear, heteroscedastic, and clustered. Additionally, it is also truncated (a cutoff score) and ...
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4 views

Multiplying odds by a Pareto RV - has this been done?

I have an agent-based/microsimulation epidemiology model. There is an individual-based parameter, which I would like to increase by a varying amount for each individual. The parameter $p \in (0,1)$ ...
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14 views

Best hypothesis test for generalized extreme value distributions?

I am trying to compare 3 non-normal distributions with some sort of hypothesis test. Data sets 2 and 3 are subsets of dataset 1 (all data). According to BIC and chi squared fitting in MATLAB, the ...
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1answer
49 views

Deegrees of freedom of Student's distribution

I'm trying to figure out the distribution of this statistic: $$S=\frac{\frac{\overline{X}-\mu_0}{\sigma / \sqrt{n}}}{\sqrt{\hat{\sigma}^2/\sigma^2}}$$ Where: $\overline{X}=\frac{1}{n} \sum_{i=1}^n ...
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13 views

Determining distribution type in Python?

What is the best way to determine what type of distribution data has in Python? I am looking at daily data and I want to be able to run some scenarios and Monte Carlo. I was using np.random.normal to ...
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2answers
271 views

Which probability distribution fits my data?

I have generated a dataset (available here) for which I try to find out the best fitting probability distribution. I first generated uniformly distributed random directions and then calculated the ...
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1answer
33 views

How to analyze crossover trial with a scale as outcome variable?

I'm working on a pilot study for a new drug. We will use a crossover design in which half of the patients will be given the drug for the first 6 weeks, then, after a washout period of one week, they ...
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1answer
44 views

How are distributions besides normal distribution used?

I just finished my first applied Stats class and learned about how are z-scores and t -statistics are used to calculate the probability under the curve. Are there other scores used for the other ...
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25 views

Adding two distributions with proportional means and standard deviations

I need to know the mean $\mu_z$ and standard deviation $\sigma_z$ of a log normal distribution $Z(\mu_z,\sigma_z)$ which is the sum of two other log normal distributions--$X(\mu_x,\sigma_x)$ and ...
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5 views

RJAGS Prediction Envelope for Distributions

I am using RJAGS to estimate the parameters of my model from data. My model contains diverse range of parameters for known distributions. I get the credibility intervals for my distribution parameters ...
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7 views

LogLogistic Reliability and MTTF for scale < 1

I am fitting the LogLogistic distribution on a Time-Between-Failure dataset, with the following expressions (referring to http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Loglogistic.pdf) $f(t) = ...
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2answers
60 views

How does the proportion of X > a compare to the proportion of Y > a?

I am completing CS109 Data Science class available online for free. I'm not quite sure what they are asking for. In general, if group A has larger values than group B on average, does this ...
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33 views

How to calculate the required sample size for x% accuracy?

I've made an algorithm for parsing some strings, and the question I have is how many random strings should I collect and test to get an estimate of how good the algorithm is? Testing on all is not ...
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7 views

Standard Error of ARPDAU

Short version: What is the ARPDAU standard error of a mobile game? Long Version: I have a mobile game and I'm tracking the ARPDAU (Average Revenue per User). $$ARPDAU_i = \frac{Total ...
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0answers
12 views

Simulate data from a custom density function with rejection sampling

I'm trying to find a solution for this problem. I want to simulate in R data from a distribution generated by a CDF like this $$F(x) = c\tfrac{\log^3(x)}{x^2}$$ or equivalently, in this case, from ...
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0answers
11 views

Methods of Spend Outlier Detection

I'm looking to formalise some logic behind outlier detection for spend categories of survey respondents during a trip or event (e.g. accommodation, meals, shopping, etc). Distributions are zero-heavy, ...
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0answers
27 views

Normalization of distributions

I am measuring intensities of structures in biological tissues, which gives a series of values for each sample. There is high variability between values for each samples from unknown procedural ...
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23 views

How to pick a good training set?

From what I understand, my training set should represent the underlying distribution of objects, but what if my local view is not such a good representation? For instance I am working on a cell (i.e ...
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28 views

Distribution over the product of three, or n, independent Beta random variables

This is a re-post of a question on the Mathematica stack exchange, as per the advice of another user (see here). I am pursuing a computational solution there, but thought it might be worth looking for ...
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56 views

Fitting one set of data with two functions

I have a set of data (42 points): ...