Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

Filter by
Sorted by
Tagged with
4
votes
1answer
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 ...
5
votes
2answers
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 ...
43
votes
3answers
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 ...
3
votes
3answers
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 $y$ ...
11
votes
3answers
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 ...
7
votes
1answer
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?
5
votes
3answers
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 ...
12
votes
2answers
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 ...
11
votes
1answer
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 ...
9
votes
1answer
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 ...
5
votes
2answers
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 ...
7
votes
3answers
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 "...
14
votes
2answers
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 ...
2
votes
2answers
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 ...
49
votes
6answers
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 ...
10
votes
4answers
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 ...
2
votes
1answer
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?
10
votes
4answers
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)...
3
votes
1answer
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 ...
9
votes
2answers
932 views

Computing the cumulative distribution of max drawdown of random walk with drift

I am interested in the distribution of the maximum drawdown of a random walk: Let $X_0 = 0, X_{i+1} = X_i + Y_{i+1}$ where $Y_i \sim \mathcal{N}(\mu,1)$. The maximum drawdown after $n$ periods is $\...
19
votes
1answer
933 views

What is the community's take on the Fourth Quadrant?

Nassim Taleb, of Black Swan fame (or infamy), has elaborated on the concept and developed what he calls "a map of the limits of Statistics". His basic argument is that there is one kind of decision ...
20
votes
3answers
5k views

Moments of a distribution - any use for partial or higher moments?

It is usual to use second, third and fourth moments of a distribution to describe certain properties. Do partial moments or moments higher than the fourth describe any useful properties of a ...
13
votes
4answers
10k views

Intuition / interpretation of a distribution of eigenvalues of a correlation matrix?

What is your intuition / interpretation of a distribution of eigenvalues of a correlation matrix? I tend to hear that usually 3 largest eigenvalues are the most important, while those close to zero ...
2
votes
2answers
1k views

How to compare different distributions with reference truth value in Matlab?

I have values from 4 different methods stored in the 4 matrices. Each of the 4 matrices contains values from a different method as: ...
4
votes
5answers
3k views

How can I determine the best fit normal distribution from this information?

I'm trying to take a normal distribution of points, and force them to become a uniform distribution. I've had little success on S.O., so I thought I'd ask here. Basically, I have a hash function ...
4
votes
2answers
485 views

Is the survival function the same as the upper tail?

Are the two synonymous? The reason I am asking is that I have a paper that calculates a certain p-value as the upper tail of the hypergeometric distribution: $\Sigma_{k}^{m} = \frac{\binom{m}{k}\...
19
votes
4answers
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?
8
votes
1answer
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 ...
84
votes
5answers
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 ...
4
votes
2answers
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 ...
11
votes
3answers
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 ...
9
votes
1answer
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, ...
13
votes
1answer
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 ...
5
votes
4answers
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 ...
50
votes
5answers
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 ...
16
votes
2answers
3k views

Why does the supremum of the Brownian bridge have the Kolmogorov–Smirnov distribution?

The Kolmogorov–Smirnov distribution is known from the Kolmogorov–Smirnov test. However, it is also the distribution of the supremum of the Brownian bridge. Since this is far from obvious (to me), I ...
4
votes
2answers
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 $n>2$?
13
votes
4answers
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 ...
22
votes
9answers
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. ...
6
votes
2answers
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 ...
2
votes
4answers
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 ...
42
votes
8answers
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.
2
votes
4answers
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 ...
2
votes
2answers
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 ...
1
vote
1answer
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 ...
14
votes
4answers
9k views

Questions about KL divergence?

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 ...
2
votes
2answers
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 ...
4
votes
3answers
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 ...
7
votes
3answers
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 ...
16
votes
5answers
4k views

Comparing the variance of paired observations

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 ...