# Tagged Questions

A distribution is a mathematical description of *probabilities* or *frequencies.*

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### Is there any PDF which satisfies the following criteria?

For an applied economics paper, I am looking for a 2-parameter probability distribution function that has the following properties: Simple, closed-form PDF $f(x)$ and CDF $F(x)$, defined on the ...
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### How to find arrival or service distribution?

I have a set of data which is inter-arrival in seconds and service time in seconds. When I try to find the distribution in Minitab all the results do not have a proper P value. I heard that you can ...
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### Estimate shifted log Gamma parameters via L-Moments

L-Moments and Probability Weighted Moments are a very robust estimation method for some cases; in particular for the Generalized Extreme Value distribution they seem to be the method of choice if it ...
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### Different histograms for same data in R and Oracle Crystal Ball

I am analysing small sample size data: >dput(dat.demand2050.unique) c(79, 56, 69, 61, 53, 73, 72, 86, 75, 68, 74.2, 80, 65.6, 60, 54) for which the ...
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### Use of Weibull model or Weibull distribution

I have a basic question regarding use of the terms "Weibull model" and "Weibull distribution". (I take Weibull as an example, but the question could apply to any distribution.) I read in books or ...
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### Unimodality of continuous univariate distributions [closed]

What are the different methods to prove that a continuous univariate distribution is unimodal? Some of them are available at Wikipedia but not much detail is given. Solution or suggestion of any ...
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### Is the product of multivariate lognormal distributions is multivariate lognormal distribution

A. Mulitivariate normal distribution case with latent variable $X$ Mapping from the low-dimensional space $X$ in Q-dimensional space (Q=2) to the high-dimensional space of $Y$ in D-dimensional space ...
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### Lack of memory (memorylessness)

The purpose of this question is to gather material about "lack of memory" and to add new ideas about that. If the conditional distribution of a given distribution is equal to unconditional ...
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### Distribution check using R

I want to check the probability distribution for my data using R.In some site I found fitdistr function in package MASS can do ...
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### How to decompose a distribution with two peaks?

I'm modeling saving account's amount, whose change looks like a log-normal distribution. It means suppose $y$ is total saving account's amount; $x = \ln(y)$ is the natural log; $dx$, the daily change, ...
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### Understanding how to get data from a dirichlet-multinomial distribution

I'm relatively new to Bayesian statistics and try to learn the fundamentals, maybe you can help. I have a three-sided die which produced in 100 trials: 45 times 1 10 times 2 35 times 3 I choose a ...
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### How to find best fit using NLMIXED in SAS

I am using Proc NLMIXED for parameter estimates and Likelihood ratio criterion of a distribution using a random sample. I have no idea about initial values, so I try different initial values to obtain ...
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### The correct probability distribution / way to identify large deviations in a set of daily changes to portfolio value

I am working on a report which is being sent through to end users that should flag to them any "large changes" in the day-to-day values for the past 30 days. These values are day-to-day differences ...
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### Properties of a particular generalization of the Gaussian-Gamma distribution

Consider the distribution $$P(x, p | \alpha, \beta, \lambda, \mu, p_0) = \mathcal{Ga}(p | \alpha, \beta) \mathcal{N}(x | \mu, \frac{1}{\lambda p} + \frac{1}{p_0}),$$ that is, a generalization of the ...
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### Conditions for positive dependence

Consider two random variables $X$ and $Y$ with joint distribution $F_{X,Y}$ and strictly positive density function $f_{X,Y}$. Additionally, let $x^*$ be the value of $x$ that solves:  ...
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### Indirect measurement of the distributions

Suppose that there is a field where cabbages grow. We have weighed all the cabbages in spring and got Gaussian distribution of weights. The same we did in autumn and got another Gaussian distribution. ...
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### Difference between null distribution and sampling distribution

I am asking this questions for clarifications on the terms between "null distribution" and "sampling distribution". I find that when some one says null distribution, actually they mean the same thing ...
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### Distribution fitting problem

I have a real data set 275, 13, 147, 23, 181, 30, 65, 10, 300, 173, 106, 300, 300, 212, 300, 300, 300, 2, 261, 293, 88, 247, 28, 143, 300, 23, 300, 80, 245, 266 and ...
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### What is the meaning of using distributions for statistical inference?

In statistics people gather a lot of data (ie heights of people or gene expression levels) to get some insight. Then in order to perform statistical analyses they try to fit their data to a ...
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### Follow up: How many counts are required to estimate a mean to a certain precision?

Having asked a question previously on the number of counts required to ascertain a sample mean to a given precision (assuming a poisson distribution) I have a follow-up question. I think my new query ...
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### How to read off 0.975 alpha value in F table

$F<(1-\alpha/2, n_x-1, n_y-1)$ and $F>(\alpha/2, n_x-1, n_y-1)$. (Testing equality of population variances). An alpha of $0.0$5 is used. $1-\alpha/2= 1-0.05/2= 1-0.025= 0.975$. However, there ...
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### Accounting for volatility in time series forecast

On the topic of forecasting, given a time series does anybody have a method to build in volatility to the response value? I have built tests around the spread and skew of the input variables by ...
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### Fitting distributions in R

I hope you are very well. I have a big dataset (~9 million registries) and I have 2 variables $X$=purchase amount and $Y$=frequency of purchase. I would like to know what distribution should I use for ...
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### How to model the distribution over payouts from aggregate (sum) data?

The setting A user is presented with a number of options related to her search query. She chooses one of them. As a result, a payout is generated. The payout lies in the range [0.05, 0.50], but the ...
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### Difficulty in calculating joint probability

I have a table. ...
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### MLE for triangle distribution?

Is it possible to apply the usual MLE procedure to the triangle distribution? - I am trying but I seem to be blocked at one step or another in the math by the way the distribution is defined. I am ...
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### How to model distributions which are not normally distributed

I would like to model the performance of a rainwater tank, which has a stochastic input (rainfall). The data are the empty volume in the tank at the end of each day. The values are skewed towards the ...
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### Approximating a Poisson distribution using a partially observed Gaussian

Note that the problem specification has changed since the original posting. Thanks to whuber for helping me better specify the question: in an attempt to make the question general, I had left out ...
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### How to deal with kurtotic interaction variable?

I'm going to do a multiple regression analysis with two continuous IVs and their interaction. I've centered the IVs and then multiplied one with another for interaction. My problem is that the ...
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### How to find the function of a skewed distribution curve by calculating k=P for 4 points along the curve

Say the minimum of k is 0 and the maximum of k is 4. k is being derived from the probability mass function, though I'm not using the formula because I do not have p of the distribution. If I have ...
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### Non-informative prior for integer restricted parameters

Does anyone have advice/references on choosing a minimally informative prior for the shape parameter of an Erlang distribution (gamma distribution with shape parameter restricted to integer space), or ...
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### Two dice problem

Two players are throwing each one die. The one that has higher value, receives a number of points equal to the difference of the values on both dice. How do you estimate probability for a winner to ...
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### Multivariate outlier analysis of data with multimodal distribution

I have a data on methylated gene expression which follows a bimodal distribution. Can I use a multivariate outlier analysis to detect differentially methylated genes? What are the various methods of ...
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### Hypothesis testing - is my distribution non random?

Say I have $n$ pairs of time series data. For each pair, I calculate a measurement which looks at the overlapping fraction of each time series pair, resulting in $n$ overlap values. EDIT : I define ...
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### How many counts are required to estimate a mean to a certain precision?

I have been photographing bubbles arriving at a fluid surface. The photographs are obtained at rate of one image per minute. Given that the frame of the image is always the same size and the source of ...
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### How to determine a statistical model to fit into data based on distribution

I am trying to learn to fit data into models.The data is multi dimensional with n observations for each of the kdimensions.I ...
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### What is a suitable probability distribution for monetary amounts?

In my Bayesian model, I have a random variable representing the amount of money received due to a user's click on an affiliate link on a website. There are several such links with different payouts; ...
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### Proper regression model for ratio data

I've been thinking about a regression model with dependent variable a ratio in the range [0-600+]. About 50%+ are 0 values though, 40%+ values [0-5], and a very small percentage of the values are ...
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### Boxplot equivalent for heavy-tailed distributions?

For approximately normally distributed data, boxplots are a great way to quickly visualize the median and spread of the data, as well as the presence of any outliers. However for more heavy-tailed ...
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### Book recommendations for beginners about probability distributions

I'm studying machine learning and every book I open I bump into chi-squared distribution, gamma-function, t-distribution, Gaussian, etc. Every book I have opened so far only defines what the ...
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### When can the variance be written as a function of expectation?

What kinds of distribution have variance as a function of expectation, i.e. let $X$ be a random variable of a distribution, $Var(X) = f(E(X))$ for some function $f$ ? Sufficient conditions including ...
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### How to test for “parallelness” of two distributions?

23 patients suffering from bruxism (grinding of teeth) have been given a treatment. Their baseline bruxism has been measured for three nights, then they were treated for 23 nights, then again the ...
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### A simple distribution problem

Suppose that $x \sim U(0, 255)$ and and $y \sim U(0, 255)$, and that $x$ and $y$ are independent. What is the distribution of $x - y$? If I were to draw 1,000 samples from this distribution, how ...
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### Jaccard Similarity - From Data Mining book - Home work problem.

Exercise 3.1.3 : Suppose we have a universal set U of n elements, and we choose two subsets S and T at random, each with m of the n elements. What is the expected value of the Jaccard similarity of ...
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### Is there a formula to determine the cumulative distribution associated with multiple different kinds of events?

Similar to this question, but with more than one different sided die. Is there a way to calculate probability distributions associated with dice, where the probability distributions for each die are ...
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### When is it ok to merge data sets [closed]

There are two variables, $x$ and $y$, with $y$ depending on $x$ somewhat. For each occurrence of $x$, I record the value of $y$ so that I get a frequency distribution for $y$ given $x$. (The ...
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### Comparing the distribution of several compositions given as percentages

I need to show that the proportion of different cell types in blood from two individuals are the same. Example: There are 6 cell types and ...
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### Quantifying a difference in probability densities

There is a range of values (V) that I'm using to calibrate a model. I'm performing a sensitivity analysis on different calibration objectives. One calibration objective, A, selects from V such that I ...
Suppose we have a model with $n$ data points and $p$ predictors. The model has an $R^2_{\text{adjusted}}=q$. What sort of distribution does the change in $R^2_{\text{adjusted}}$ have when a random ...