Questions tagged [distribution-identification]

Questions about recognizing a probability distribution from a figure, formula, or text description. Please use a specific, informative title.

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169
votes
2answers
228k views

How to determine which distribution fits my data best?

I have a dataset and would like to figure out which distribution fits my data best. I used the fitdistr() function to estimate the necessary parameters to ...
33
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3answers
25k views

What distribution does my data follow?

Let us say that I have 1000 components and I have been collecting data on how many times these log a failure and each time they logged a failure, I am also keeping track of how long it took my team to ...
23
votes
3answers
2k views

Does this distribution have a name? $f(x)\propto\exp(-|x-\mu|^p/\beta)$

It occurred to me today that the distribution $$ f(x)\propto\exp\left(-\frac{|x-\mu|^p}{\beta}\right) $$ could be viewed as a compromise between the Gaussian and Laplace distributions, for $x\in\...
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. ...
12
votes
1answer
223 views

Name for a distribution between exponential and gamma?

The density $$f(s)\propto \frac{s}{s+\alpha}e^{-s},\quad s > 0$$ where $\alpha \ge 0$ is a parameter, lives between the exponential ($\alpha=0$) and $\Gamma(2,1)$ ($\alpha \to \infty$) ...
11
votes
2answers
729 views

What kind of distribution does this have?

Currently I'm trying to figure out the distribution of the following: $X \sim \frac{\sqrt{n}}{\sqrt{Gamma(n,\beta)}}$ where the denominator follows a $Gamma(n,\beta)$ distribution. I've checked out ...
11
votes
1answer
4k views

Distribution of the ratio of dependent chi-square random variables

Assume that $ X = X_1 + X_2+\cdots+ X_n $ where $X_i \sim N(0,\sigma^2)$ are independent. My question is, what distribution does $$ Z = \frac{X^2}{X_1^2 + X_2^2 + \cdots + X_n^2}$$ follow? I know ...
8
votes
0answers
332 views

Distribution with a given moment generating function

As a follow-up to a question on a central limit theorem for independent random variables (r.v.) here, let $Y_j=-\log(1-V_j)$, where $V_j\sim\mbox{beta}(1-\sigma,j\sigma)$, $j\in\mathbb{N}^*$, $\sigma\...
7
votes
2answers
604 views

Identifying the following distribution

I have a distribution, which I initially assumed to be a Rayleigh, but it almost certainly isn't. Before I consider convolutions of various distributions, e.g. Rayleigh convolved with Boltzmann, ...
6
votes
2answers
6k views

Understanding the Cullen and Frey plot

I would like to figure out which distribution fits my data best. Here is the histogram of my data : I used the fitdistrplus package in R to try to find the best ...
6
votes
2answers
281 views

Can anyone suggest a distribution for this histogram

I have some data and I am trying to identify its distribution. The nearest I can get is a skewed-Gaussian distribution, but I don't think it is. The data itself consists of 130000 points and is binned ...
5
votes
3answers
246 views

What kind of distribution is this? (Number of stones until 2 are adjacent in a game of Go)

I've plotted the histogram of the number of stones required so that 2 are adjacent when randomly placed 1 by 1 on a goban (think of a 19x19 chessboard and I place pieces 1 by 1 until 2 are adjacent, ...
4
votes
3answers
496 views

What kind of distribution is this “almost” uniformly distributed data for calls/week?

My supervisor asked me to find out which distribution represents a particular situation. I have a VoIP generator that generates calls "uniformly" distributed between callers. This means that the ...
4
votes
2answers
2k views

How to determine the type of probability distribution for a dataset?

I have aggregated(total) youtube videos views. I have take log of that views. And calculated autoregressive koefs that can be used for the video views predictibility tests. Let say I have aggregated ...
4
votes
1answer
71 views

What is the name of this distribution?

I came across this: a categorical distribution with $K=10,000$ parameters (categories), and we take only few samples from this distribution, say $N=400$ (the point is $N < K$). Now, obviously, not ...
4
votes
1answer
285 views

What is this distribution? (time-delays between two events)

I have a right-skewed distribution that has this qq-plot against a normal with the same mean and standard deviation: The data are time-delays between two events. Also, this is the histogram of the ...
4
votes
0answers
315 views

Distinguish between distributions

I have the following data frame and want to know what distribution is consistent with it. ...
3
votes
1answer
453 views

Is there a common underdispersed discrete distribution with unbounded support for general mean and variance?

I have a mean $\mu$ and a variance $\sigma^2$ with underdispersion, i.e., $\sigma^2<\mu$. Is there a standard discrete distribution with these moments and unbounded-on-the-right support, i.e., ...
3
votes
2answers
328 views

What does the distribution of bootstrapped values in this Cullen and Frey Graph tell me?

I am trying to find a suitable distribution to describe my data, and as one of the first few steps I created a Cullen and Frey Graph using the descdist command from ...
3
votes
2answers
78 views

Estimating the blockchain mining time for $N$ nodes

I am trying to simulate a set of times for the below problem. There are N nodes. Each node generates a random number($R$) in the range $[0,K]$ per second. Guess the time it takes by each node to ...
3
votes
1answer
139 views

Name this distribution!

While looking for a link function for my model I realized I cannot find a good fit for the distribution of my Y (see fig. below). It is the distribution of number of offspring for a given season, the ...
3
votes
0answers
169 views

What distribution has the p.d.f. of form $\frac{e^{-b \cdot x} \cdot x^c}{1 + e^{-k \cdot (x+a)}}$ for $x >0$ and parameters $b > 0, k > 0, c > 0$?

In my work I met the p.d.f. of form $$p(x) \propto \frac{e^{-b \cdot x} \cdot x^c}{1 + e^{-k \cdot (x+a)}}$$ with support $x \in [0, +\infty)$ and positive parameters $b > 0, k > 0, c > 0$. ...
3
votes
0answers
74 views

Is this a known distribution?

For work, I plotted a set of shops by how many times they did business in the past week. The plot I got out looked something like this: This looked obviously like a Pareto distribution. After all, ...
2
votes
1answer
123 views

Are the data in this figure normally distributed?

What kind of distribution is figure 2 in this study? If it's a Gaussian distribution for the LH hormone, I can't make any sense of the data. The article: Aksglaede, L. et al. (2009): Recent decline ...
2
votes
2answers
73 views

Fitting a distribution like exponential but with always negative $\frac{d^2}{dx^2} \log \text{pdf}(x)$

I have some continuous data in the domain $[0,\infty]$ which I have physical reason to believe is almost, but not quite exponentially distributed. The difference between my idea of a distribution and ...
2
votes
1answer
88 views

Identifying a distribution

I am trying to understand what sort of distribution is produced by the following code. Using the following Matlab code we can generate a distribution (normalized such that the sum of the set is equal ...
2
votes
1answer
222 views

What is this distribution? $(x-1) \theta^2 (1-\theta)^{x-2}$

Does anyone know what the following distribution is, please? I can tell it is discrete and $\theta$ is somehow a probability. Thank you! $$\mathbb P_X(x; \theta) = (x-1) \theta^2 (1-\theta)^{x-2}, \ \...
2
votes
2answers
158 views

How to determine the distribution iof this transformed variable $X_c = X ({1_{\{|X|>c\}}}-{1_{\{|X|\le c\}}})$

I have one question from econometric class which asks to find the probability distribution of the following: $$X_c = X ({1_{\{|X|>c\}}}-{1_{\{|X|\le c\}}}) $$ where $X \sim N(0,1)$ and $c > 0$...
2
votes
1answer
75 views

$X_i + X_i^2$ where $X_i \sim$ normal; what is the distribution?

$X_i + X_i^2$ where $X_i \sim$ normal. Does this sum have any particular distribution?
2
votes
2answers
568 views

Distribution of values in a time series (tidal data)

I was trying to help my colleague with fitting a distribution curve to some empiric data (these are sea water level observations at different time points). However, I haven't succeeded since it's my ...
2
votes
3answers
116 views

How long is a distribution considered normal?

I have a dataset of metric distances ($n=5800$) and plotted those as a histogram. My initial thought was that this distribution looks normal. But after performing a Shapiro Wilk test and plotting the ...
2
votes
2answers
98 views

What kind of frequency distribution is this?

I have a discrete frequency distribution, that looks like this I am trying to find what type of distribution is it? I looked at many models but it does not seem to comply with any. I have 345 ...
2
votes
1answer
27 views

Modeling Smooth Decay on Logarithmic Y

I have an empirical distribution that looks like the the image below and I hoping to model it with some parametric distribution. The X axis measures "number of ...
2
votes
0answers
28 views

What's the name for a distribution where at the extreme there are more values farther away from the mean than closer?

The image below from this blog provides a good example. I'm talking about distributions that are roughly Gaussian except that there are more values at the high end that would be expected. In ...
2
votes
0answers
34 views

Is there a name for this simple discrete distribution? [duplicate]

I'm just wondering if there's a name for the distribution described by the following p.m.f.: $$p(n) = n(1-s)^{n-1}s^2$$ where $n$ is an integer from $1$ to $\infty$ and $0\lt s\lt1$.
2
votes
0answers
209 views

What is the name of the distribution whose support is (0,1) and whose pdf kernel is exp(ax) - 1?

Does this probability distribution have a name? $$f_a(x) dx = \frac{a}{e^a-(a+1)} \left(e^{a x} - 1\right) dx, \quad 0 \le x \le 1.$$ Edit: I want $a$ to be positive. I don't think this is what is ...
1
vote
1answer
27 views

What is the name and formalism of this discrete distribution? [closed]

I am searching the name of something similar to a binomial distribution, but with individual probabilities (P(1) to P(N)). I calculated (brute-forced with a script) the probability of k positive ...
1
vote
1answer
141 views

What distribution is this? (time until task completion and submission)

I am looking at submission data—the length of time it takes for someone to complete a flow which involves submitting an item of content. I am getting the following distributions. I have two ...
1
vote
1answer
18 views

calculate mean of normal distribution given SD and probability corresponding to a single range

Suppose that I have a normally distributed variable with unknown mean and known SD: $X \sim N(\mu, 1)$. I also know that $P(-2 < X < 2) = 0.3.$ Is it possible to calculate $\mu$ from this ...
1
vote
1answer
43 views

Let $f_X(x)= \frac{x^2e^{-\frac{x^2}{2}}}{\sqrt{2\pi} } 1_{(-\infty,+\infty)}$, what is this distribution called?

Let $$f_X(x)= \frac{x^2e^{-\frac{x^2}{2}}}{\sqrt{2\pi} } 1_{(-\infty,+\infty)},$$ is the pdf of random variable $X$. What is this distribution called? I only know $f_X(x)\propto x^2e^{-\frac{x^2}{2}} ...
1
vote
0answers
31 views

What probability distribution would be look like this?

I was playing with R, I started with adding consecutive binomials (the n parameter of the second binomial variable depends of the result of the first binomial and so on...). After a few more ...
1
vote
0answers
22 views

Identifying the best fitting distribution type to test

Hi I tried to analyze a dataset, of USDT concurrency and following is the frequency distribution I received for log return I need this dataset to fit for a particular distribution. Can we suggest ...
1
vote
3answers
897 views

How to determine which distribution fits my data set?

I have this data set which I am trying to find which distribution my data set can be accurately represented by using r. I performed the Shapiro-Wilk test and found that my data does not come from a ...
1
vote
0answers
41 views

Identifying the distribution of this data

I'm working with a datetime series, and each observation is the count of occurrences per that period. This sounds to me like these values would be Poisson distributed. But my EDA has left me ...
1
vote
0answers
56 views

What is the distribution of this Random Variable? I am expecting a Chi-Squared, but there is one term which is extra

I am trying to find the distribution o random variable $H$, but I am somehow confused. The assumption is $M$ and $N$ are large enough (maybe around $100$). When $L=1$, the distribution of $H$ is a ...
1
vote
0answers
64 views

Identify the underlying distribution from multiple samples

I have $30$ unequal samples ($n_i >1000$) from a supposedly same population. How should I go about identifying the underlying distribution of the population using these $30$ samples simultaneously? ...
1
vote
0answers
27 views

Distribution of relative proportions of draws from two uniform distributions

Drawing samples from 2 uniform distributions and calculating pairwise proportions of drawn values gives rise to a distribution I cannot recognize. What distribution is this? ...
1
vote
0answers
143 views

Determining the distribution of data

Hi, I am a student learning financial modelling. I would like some help in determining the distribution of the data given the plots above. I am reluctant to assume normal distribution of the data due ...
1
vote
0answers
296 views

What distribution should my data on sales follow

I'm a chain store and have many stores across the country that all sell a particular shampoo product P. I have made a plot as shown in the image below. For example, 30 stores each sold 1 of P in the ...
1
vote
0answers
382 views

What are alternatives to uniform distribution when trying to fit observed data distribution? [closed]

I have a dataset of 500 observations and I have to find the best fitting distribution. If I look at the histogram of the data and the QQ plot my data seems to follow an uniform distribution. But a chi-...