A distribution is a mathematical description of probabilities or frequencies.

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Confirming calculations with simulations?

This question may be a little abstract, but I would like to understand how to develop a mentality towards performing statistical simulations. For example: If I have a normal distribution, and I ...
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How to reconstruct moments from aggregated data?

Let $X_{1\ldots n}$ be a stochastic variable that is log-normal distributed, with parameters $\mu$ and $\sigma$. Now suppose all $X_i$ are aggregated into $Y_{1\ldots m}$ where $Y_1$ is the mean of ...
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Expected time in exponential distribution?

I'm using the exponential distribution to calculate a probability of an event to occur. $\lambda = 0.007$ failures/year. I am to calculate an expected time between 2 failures. My approach was to ...
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29 views

Which distribution is correct in modeling conversion rate in a Monte Carlo

I am building a model for a Monte Carlo simulation that estimates the number of sales made for a door-to-door salesman. Looking at his historic success by city, it seems he converts about 80% +/- 20% ...
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Cumulative Function Values [on hold]

I'll have an exam next Thursday, I'm studying for the exam but I got a doubt in one exercise. Thats it: Given this values: 2.5, 3.6, 5.7, 8.3 and 1.0 determine if or not the values follow this ...
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34 views

which distribution to expect for interval counts

It is my first question here and I am not a statistian. So - I am sorry for any mistake - please correct me. I have data from measuring a feature of a number of entities (continious data). As I don't ...
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20 views

What is the distribution of a normalised (scaled) poisson distribution?

I have 5 groups of very different sizes. I want to know if various attributes are the same for the groups when I have corrected for the differences in size, e.g. ...
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25 views

Variance of compound distribution

The binomial distribution describes the probability of $k$ 'success' events given $N$ independent trials, each with a probability $p$ of being a success. The distribution is described by the formula ...
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How to test two paired probability distributions

I have 50 paired samples, each sample contains the proportion of animals per length category, collected from the same source using either method A (50 samples) or method B (50 samples). Now I would ...
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what does value of t test mean? [duplicate]

I have two distribution of one variable and I've used t test to find how much they are significantly different. But I'm not very familiar with this test and don't know what does this values mean? is ...
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19 views

chi-squared to test if two variables have the same frequency distribution

I want to test if x and y have the same frequency distributions using chi-squared. In my code below, I've concluded that because ...
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Order Statistics Conditional Distribution of Affiliated System

We have a system with $M (M\ge 2)$ random variables. The M variables are related as follows. For each i, 1 to M, $X_i = I_i+Z$, where $I_i$, Z are independent uniform random variables. What is the ...
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Testing whether sampling (convex polytope) is uniform

Currently, I am sampling points from: i) a convex polytope (i.e. Ax <= b) ii) a high dimensional simplex The algorithms I am using are hit-and-run and a simple version of Bayesian bootstrap. I ...
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+100

Information about normal distribution

Is it fair to assume that this values have a normal distribution? Frequency of clock of a CPU [I have 100 observations between 100 Mhz and 4Ghz] Ram of a Computer [I have 150 observations between ...
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29 views

What would be more flexible alternative to the Dirichlet distribution that is still “nice”?

Let's assume that I have some measurements about the total mass of certain compound. These measurements are very accurate so let's assume that the mass is just 1 (unit) in each case. Then I know that ...
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Fitting poweRlaw distributions in R [closed]

Sorry for a newbie question, i have a dataset having centralities of a network, i want to fit poweRlaw distributions on data. My dataset (Centralities) have alot of zeroes except "Degree centrality". ...
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Simulating random variables given partial distributions and correlation

After Monte Carlo simulations I obtained approximated distributions for X and Y. Now I want to add some form of correlation between them. To simulate random variables from a distribution the idea is ...
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How large does a Poisson distribution's mean need to be to use normal distribution statistics?

As the mean of a Poisson distribution increases, the Poisson distribution approximates a normal distribution. I assume that once the Poisson mean becomes large enough, we can use normal distribution ...
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Estimating the parameters of a Beta distribution using the sample average and standard deviation

This is a simple question, but I just want to be sure. Imagine that we have a sample of $n$ data $\{x_1, \dots, x_n\}$ and that we want to fit them to a Beta distribution. Imagine that we have ...
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50 views

Area under ROC given the two distributions

I have two distributions p1 and p2 (generating in R using distr package), and I want to compute the area under the ROC curve. To construct the ROC curve, I have to compute the probability of detection ...
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Distribution for an operation of variables with identical distributions

I have this doubt: Consider $X$~$N(\mu_X,\sigma^2)$, $Y$~$N(\mu_Y,\sigma^2)$ and $Z=X-Y$ I know that $E(Z)=E(X)-E(Y)=\mu_X-\mu_Y$ because the expected value is a linear operator. And I know ...
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Simulating lognormal data - not just log(mean) and log(sd)?

According to this question, to simulate a log-normal dataset with a mean and SD known, you just enter log(mean) and log(sd). For example, lets say I wanted a mean of 5 and SD of 2. ...
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Am I breaking the assumptions of the Poisson distribution?

The Poisson distribution arises when events are counted within a specified interval. I've recorded the number of events each month (I'll not discuss what these events represent). This appears to meet ...
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Lognormal distribution using normal distribution inputs

I'm simulating lognormal data in R log(Y), using the mean and standard deviation of Y. This article outlines it very well! One step in the article I'm having trouble solving how it works though. ...
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37 views

Find the values between percentiles in a frequency distribution

In the distribution below, how would I find the values that lies between 30% and 50% of the distribution? R code would be handy but not essential! 28, 28, 29, 30, 30, 31, 31, 31, 31, 32, 32, 32, 34, ...
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On the Beta-t-EGARCH and the score

I am going to define the Beta-t-EGARCH model utilizing the more familiar GARCH model as does Harvey in Dynamic models for volatility and heavy tails (2008), I hope this will serve the purpose to ...
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Bhattacharyya Distance for Age/Gender Groups?

I'm calculating distances for groups based on Age/Gender Compositions (to rank their similarity in demographic composition.) I'm working with the following: Men 18-34, Men 35-49, Men 50-64, Men 65+, ...
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How to measure the difference of a distribution being normally distributed

Imagine I have a distribution like the following File SkewedDistribution.png of Wikimedia Commons by User:Audriusa licensed under CC-BY-SA 3.0 Now I want to measure, how this distribution differs ...
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Relationship between distributions and hypothesis testing

Here on chi-squared distribution wikipedia page is mentioned that many statistical tests use chi-squared distribution. I would like to ask why? What is so special about chi-squared that predetermines ...
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The score of a dynamic model is a martingale difference sequence

I am going to write down some parts of Dynamic models for volatility and heavy tails by Andrew Harvey (2008) with my comments in bold and then ask for an alternative explanation of the final part. ...
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rnorm vs dnorm in R

In human language the rnorm(n=1000, m=24.2, sd=2.2) returns the random numbers which follows normal distribution. Another explanation could be that it returns ...
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How to calculate mean, median, mode, std dev from distribution

How to calculate mean, variance, median, standard deviation and modus from distribution? If I randomly generate numbers which forms the normal distribution I've specified the mean as ...
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The relationship between cumulative distribution vs cumulative density vs probability density

Can you please explain those three terms and the relationship between them (both graphical and mathematical way would be fine)? EDIT: Those terms are mainly associated with functions.The quotation ...
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What are quantities when used in distribution functions?

What are quantities in distribution functions? I've seen this term but googling shows up various (for me unrelated) results and I have trouble to categorizing it somehow. What should I imagine when ...
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Logistic regression and normal distribution of predictors

I have a question and I hope someone can help me with my confusion. I want to run a univariable logistic regression model to see whether my predictor (which is not normally distributed, but also not ...
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What is the problem with statistical outlier detection approaches if we have distribution of attributes?

A group of outlier discovery methods are statistical approaches. Two drawbacks mentioned for statistical methods in many books and papers: They can apply just on a single attribute We need to know ...
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How to determine similarity between histograms? (Which metric to use?!)

Hello Stack Exchange community, I'm relatively confused on what to do in this scenario. I am running an experiment that retrieves data of interest and stores it as an array. Experimental conditions ...
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Intuition for this observation//how restrictive is this assumption?

For many common continuous unimodal distribution function $F$ with density $F'$, I find that the derivative (wrt $x$) of $$(1)\quad \frac{F'(x)}{F''(x)}$$ i.e. $$\frac ...
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How accurate is my simple description of a confidence interval?

Here's my simple words-only description of a 95% confidence interval for the mean. How accurate is it? the sample mean comes from a distribution of possible sample means the sample mean might have ...
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60 views

Approximating the distribution of a linear combination of beta-distributed independent random variables

This question is related with these other two questions in Cross Validated, which has been already answered: Approximate the distribution of the sum of ind. Beta r.v Central limit theorem when the ...
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Predicting water levels based on rainfall stats

I am curious if R or any other open source code can deal with forecasting changes in water elevation based on a predicted/forecasted value of rain. I have a ton of data that shows water elevations ...
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Get quantile function of dynamic mixture model

I have a dynamic mixture distribution fitted to my risk data (i.e., I have all parameters) of Weibull and Generalized Pareto, with a Cauchy CDF mixing function, that can be written as: $mixture(x): ...
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Compare distributions in time series

I have a time series (weekly sales data), on which i have made an intervention analysis (to be specific a VARIMAX). The intervention (increased opening hours) ended out being insignificant. But what i ...
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How to calculate log-normal distribution parameters with partial data?

Imagine we have a partial data and we know that this partial data represent only the left 5% of the log-normal distribution, which the overall data follow. How can we calculate the mean-log and sd-log ...
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How to compute the likelihood of a sample within a process containing gaussian and Non-gaussian noise

First, I'm sorry if the topic doesn't reflect the essence of my question very well, I don't have a very good statistical background. I've got a random variable, that is subject to two sources of ...
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Incorporating uncertainty in hypergeometric probability test

Wikipedia's page on determining the hypergeometric probability describes the variables in the following way: N is the population size, K is the number of success states in the population, n ...
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What are the criteria to choose for a bootstrapping, frequency, forecasting of fitting method to fit demand data?

My goal is to calculate the inventory height of several products. To do so, I have to calculate the probabillity a certain demand occurres. However to determine the distribution based on historical ...
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What is a common minimum support value for the Apriori algorithm in the wild?

The data set I am working with at the moment requires a minimum support value of 0.00001 in order to return any results. This seems awfully low. I believe it's due to the fact that there are tens of ...
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Conditions to be a Joint Discrete Distribution Function

I am reading a paper on modeling the dependencies in discrete distribution functions, and am having a hard time understanding the following. Let us define: $$r \leq min(p,q)$$ $$ B(u,v) = ...
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Why doesn't a sample proportion also have a binomial distribution

In a binomial setting, the random variable, X, that gives the number of successes is binomially distributed. The sample proportion can then be calculated as $\frac{X}{n}$ where $n$ is your sample ...