Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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463 views

Sampling with unequal bins?

I have a very simple model. This model uses data that are not given as continuous distributions, but are described by percentiles. What is the best way to sample these percentile bins, when the bins ...
9k views

How can the IID assumption be checked in a given dataset?

1- How can I check if a set of data can be assumed as IID data? I'm not so familiar with statistics, but I guess I should look at the first lag of autocorrelation for independent distribution. Have no ...
17k views

Empirical relationship between mean, median and mode

For a unimodal distribution that is moderately skewed, we have the following empirical relationship between the mean, median and mode: $$\text{(Mean - Mode)}\sim 3\,\text{(Mean - Median)}$$ How ...
465 views

Does data transformed in a certain way from a normal distribution fit some other common distribution?

I have sampled a number of $x$ values from a normal distribution with mean 0 and sd 0.2. I then transformed these $x$ values to $y$ values using the formula $y = e^x/(e^x + 1)$. I know that the $y$ ...
272 views

Approximating $Pr[n \leq X \leq m]$ for a discrete distribution

What's the best way to approximate $Pr[n \leq X \leq m]$ for two given integers $m,n$ when you know the mean $\mu$, variance $\sigma^2$, skewness $\gamma_1$ and excess kurtosis $\gamma_2$ of a ...
539 views

A measure to describe the distribution of a dendrogram

Could anyone suggest some statistical measures to describe the distribution of a dendrogram? If I have two dendrograms, how could can I quantify their structural differences?
740 views

Expected distribution of random draws

I have a two part question; First Part: I have an urn with 20 balls, 2 of those balls are purple, and I pull out 6 balls at random. I witness 100 realizations of this process. Given the observed ...
7k views

How to parameterize the ratio of two normally distributed variables, or the inverse of one?

Problem: I am parameterizing distributions for use as a priors and data in a Bayesian meta-analysis. The data are provided in the literature as summary statistics, almost exclusively assumed to be ...
2k views

Why Use the Cornish-Fisher Expansion Instead of Sample Quantile?

The Cornish-Fisher Expansion provides a way to estimate the quantiles of a distribution based on moments. (In this sense, I see it as a complement to the Edgeworth Expansion, which gives an estimate ...
5k views

Product of beta distributions

I am looking at trigger efficiencies, meaning that I have some device that fires on $k$ out of $n$ events. In the end I am interested in some estimate of the efficiency $\epsilon$ which is the ...
611 views

Is there an analytical expression for the distribution of the max of a normal k sample?

For example: k <- 100 R <- 10000 max.g <- numeric(R) for(i in 1:R) max.g [i] <- max(rnorm(k)) hist(max.g) # We can see it's right tailed... I ...
4k views

Distance between empirically generated distributions (in R)

I'm not a statistician, but I sometimes need I play around with data. I have two data sets, lists of values in the unit interval. I've plotted them as histograms, so I have an intuitive idea of how "...
3k views

Trigonometric operations on standard deviations

Addition, subtraction, multiplication and division of normal random variables are well defined, but what about trigonometric operations? For instance, let us suppose that I'm trying to find the angle ...
3k views

How can I display empirical pdf of my 100x1 vector data in Matlab? [closed]

I have a data which is 100x1 vector. How can I display its empirical pdf in Matlab? Also, if I want to compare the pdf of three vectors on the same graph, then how to do that? Right now I am using ...
227k views

How to perform a test using R to see if data follows normal distribution

I have a data set with following structure: a word | number of occurrence of a word in a document | a document id How can I perform a test for normal ...
4k views

How to look for valleys in a graph?

I'm examining some genomic coverage data which is basically a long list (a few million values) of integers, each saying how well (or "deep") this position in the genome is covered. I would like to ...
695 views

How do you calculate the standard deviation on a multiplicative scale for a distribution that has been transformed logarithmically?

I know the value for the 16% quartile, so I know the additive deviation for the given distribution. How do I find the deviation of the log of the given distribution on a multiplicative scale?
2k views

Quantifying QQ plot

The qq-plot can be used to visualize how similar two distributions are (e.g. visualizing the similarity of a distribution to a normal distribution, but also to compare two artibrary data distributions)...
800 views

Using Lorenz curve / Gini coefficient for (non-ecomoical) distribution data

I have distributional data which I represent as a density. The data represents frequencies of user activities on a computer screen (e.g. amount of clicks on the y or x-axis of that screen but also ...
932 views

52k views

Difference between histogram and pdf?

If we want to visibly see the distribution of a continuous data, which one among histogram and pdf should be used? What are the differences, not formula wise, between histogram and pdf?
209 views

Estimating parameters of sum-stable RV via L-estimators

One of the purported uses of L-estimators is the ability to 'robustly' estimate the parameters of a random variable drawn from a given class. One of the downsides of using Levy $\alpha$-stable ...
196k views

Relationship between poisson and exponential distribution

The waiting times for poisson distribution is an exponential distribution with parameter lambda. But I don't understand it. Poisson models the number of arrivals per unit of time for example. How is ...
1k views

Computing probability distribution function for uniform random variables and Y=1-X

X is uniform random variable in [0,1] and Y=1-X. How do I calculate the distribution function F(X,Y)? I can see that Y is also uniformly distributed and can draw the intervals. But I am unable to ...
3k views

Estimating mean and st dev of a truncated gaussian curve without spike

Suppose I have a black box that generates data following a normal distribution with mean m and standard deviation s. Suppose, however, that whenever it outputs a value < 0 it does not record ...
4k views

The distribution of the linear combination of Gamma random variables [duplicate]

If $X_i\sim\Gamma(\alpha_i,\beta_i)$ for $1\leq i\leq n$, let $Y = \sum_{i=1}^n c_iX_i$ where $c_i$ are positive real numbers. Assume all the parameters $\alpha_i$'s and $\beta_i$'s are all known, ...
2k views

Testing two independent samples for null of same skew?

What tests are available for testing two independent samples for the null hypothesis that they come from populations with the same skew? There is a classical 1-sample test for whether the skew equals ...
2k views

How to draw a probable outcome from a distribution?

I have collected positional data. To visualize the data, I'd like to draw a 'typical' outcome of an experiment. The data comes from a few hundred experiments, where I identify a variable number of ...
52k views

If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?

I'm sure I've got this completely wrapped round my head, but I just can't figure it out. The t-test compares two normal distributions using the Z distribution. That's why there's an assumption of ...
3k views

Why does the supremum of the Brownian bridge have the KolmogorovāSmirnov distribution?

The KolmogorovāSmirnov distribution is known from the KolmogorovāSmirnov test. However, it is also the distribution of the supremum of the Brownian bridge. Since this is far from obvious (to me), I ...
274 views

What is the distribution of $\chi^n_k$?

$\chi^n_k=\sum_{i=1}^kx_i^n$ where $x_i$ are Gaussian variables and $n>2$?
12k views

What is the distribution of OR (odds ratio)?

I have a bunch of articles presenting "OR" with a- 95% CI (confidence intervals). I want to estimate from the articles the P value for the observed OR. For that, I need an assumption regarding the ...
6k views

How do I figure out what kind of distribution represents this data on ping response times?

I've sampled a real world process, network ping times. The "round-trip-time" is measured in milliseconds. Results are plotted in a histogram: Ping times have a minimum value, but a long upper tail. ...
424 views

How to limit my input data for Jaccard item-item similarity calculation?

I'm trying to compute item-item similarity using Jaccard (specifically Tanimoto) on a large list of data in the format (userid, itemid) An item is considered as ...
563 views

Ranking distributional data by similarity

The question in short: What methods can be used to quantify distributional relationships between data when the distribution is unknown? Now the longer story: I have a list of distributions and would ...
55k views

How can I test if given samples are taken from a Poisson distribution?

I know of normality tests, but how do I test for "Poisson-ness"? I have sample of ~1000 non-negative integers, which I suspect are taken from a Poisson distribution, and I would like to test that.
411 views

Modeling success rate with gaussian distribution

In many papers I see data representing a rate of success (i.e a number between 0 and 1) modeled as a gaussian. This is clearly a sin (the range of variation of the gaussian is all of R), but how bad ...
916 views

Density function for a multivariate Bernoulli-like distribution

I'm looking for a distribution to model a vector of $k$ binary random variables, $X_1, \ldots, X_k$. Suppose I have observed that $\sum_i X_i = n$. In this case I do not want to treat them as ...
424 views

Approximating density function for a non-normal distribution

My question is actually quite short, but I'll have to start by describing the context since I am not sure how to directly ask it. Consider the following "game": We have a segment of length n ("large ...
9k views

I am comparing two distributions with KL divergence which returns me a non-standardized number that, according to what I read about this measure, is the amount of information that is required to ...
2k views

What would the calculated value of the standard deviation of a uniform distribution be?

A colleague wants to compare models that use either a Gaussian distribution or a uniform distribution and for other reasons needs the standard devation of these two distributions to be equal. In R I ...
2k views

Is Spearman's correlation coefficient usable to compare distributions?

I have distributions from two different data sets and I would like to measure how similar their distributions (in terms of their bin frequencies) are. In other words, I am not interested in the ...
1k views

Nonhomogeneous Poisson and Heavy tail inter arrival time distribution

What is the relationship between a Nonhomogeneous Poisson process and a process that has heavy tail distribution for its inter arrival times? Any pointer to a resource that can shed some light on ...
I have $N$ paired observations ($X_i$, $Y_i$) drawn from a common unknown distribution, which has finite first and second moments, and is symmetric around the mean. Let $\sigma_X$ the standard ...