A distribution is a mathematical description of *probabilities* or *frequencies.*
3
votes
1answer
101 views
Spacings between discrete uniform random variables
Let $U_1, \ldots, U_n$ be $n$ i.i.d discrete uniform random variables on (0,1) and their order statistics be $U_{(1)}, \ldots, U_{(n)}$.
Define $D_i=U_{(i)}-U_{(i-1)}$ for $i=1, \ldots, n$ with ...
0
votes
0answers
43 views
When to use the raw dataset as opposed to a transformed dataset for computing divergence?
Let us assume I have a set of observations:
Dataset 1: Raw
$A = [a_1,a_2,a_3,a_4,...]$
$B = [b_1,b_2,b_3,b_4,...]$
One assumptions before I proceed: Range of the values that the random variable ...
1
vote
1answer
51 views
What's another word for “tails” when referring to distributions?
What's another word for "tails" when referring to the narrow ends of distributions?
Or is there another word for distribution tails?
It seems like I heard something else used before (e.g., x ...
1
vote
1answer
93 views
Inter quartile range and outliers in boxplot with logarithmic y-axis
Let's say I have a set of data which are lognormal-distributed and I want to
create boxplots. The part of the values which is symbolized by the box may lie somewhere around 1. In that case, the inter ...
2
votes
3answers
2k views
How does the sampling distribution of sample means approximate the population mean?
I am trying to learn statistics because I find that it is so prevalent that it prohibits me from learning somethings if I don't understand it properly. I am having trouble understanding this notion of ...
36
votes
4answers
2k views
What is intuition behind beta distribution?
Disclaimer: I'm not statistician but rather software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
0
votes
0answers
34 views
Flexible multivariate parametric density
Suppose I have observed a vector-valued data point $y_{obs}$ from a statistical model:
$$
y \sim f(\theta)
$$
where $\theta$ are the unknown model parameters.
I would like to estimate $\theta$, but ...
4
votes
0answers
66 views
Transforming two normal random variables
I'm reviewing for a test, and I am not sure if I am getting the right solution.
Let $X$ and $Y$ be iid $\mathcal{N}(0, \sigma^2)$ random variables.
a. Find the distribution of $U = X^2 + Y^2$, $V = ...
0
votes
0answers
8 views
Can significance be determined from data on individual companies in different industries?
I have gross margin data from 20 different industries (each industry has 20 to 60 companies). Within each industry, at least one company used a new production system (about 30 companies use the new ...
1
vote
2answers
107 views
How can I use KL-divergence to weight features?
I have a naive Bayes classifier with two classes (target and non-target) and distributions for a number of features (the same for both classes).
I know that some features contribute more, or less to ...
-1
votes
2answers
210 views
Best book to learn probability - poisson, binomial, regression, etc
What is the Best book to learn probability - poisson, binomial, regression, etc.
I am working as an odds adjuster at a bookmaker and need to advance my skills to an odds compiler level.
1
vote
0answers
42 views
Is there a KS test for panel data?
Wikipedias says
In statistics, the Kolmogorov–Smirnov test (K–S test) is a
nonparametric test for the equality of continuous, one-dimensional
probability distributions that can be used to ...
2
votes
0answers
152 views
Statistical distance of arbitrary multivariate distributions
What meaningful statistical distance measure can be used for computing in a meaningful way a distance between two arbitrary multivariate probability distributions? I am interested in doing this ...
1
vote
1answer
92 views
Cluster analysis with skewed distibutions
For my master's thesis I would like to use different clustering algorithms to cluster municipalities (as objects) in regard to their land-use characteristics (as variables).
Analyzing my data ...
4
votes
2answers
109 views
Randomly picking from $n$ choices roughly $n$ times. What's the resulting frequency distribution called?
Not sure of the best way of phrasing this question, but I'll give it a go.
If I were to randomly choose whole numbers between 1 and $n$ a significant number of times relative to $n$ (say, $m$, where ...
2
votes
1answer
201 views
Derivation of Rayleigh-distributed random variable
I only have a uniform distribution function between [0,1]. And from this distribution, I should generate a sequence of Rayleigh distributed random variable using some software.
Anyhow, I was able to ...
0
votes
0answers
7 views
How to determine preference for x/y on the basis of proportions?
I would like to determine the preference for a certain strategy category on the basis of proportions. This is my setup:
respondent reads scenario
than the respondent chooses x strategies out of 8 ...
1
vote
1answer
170 views
real example of multinomial distribution
I found multinomial distribution really powerful in theory. But I don't if my real case can be treated as multinomial. there are two cases:
1. there are n students, 30% chose apple, 40% chose banana, ...
4
votes
1answer
71 views
Luck or skill in 3-person game
Two friends and I have been playing a game that is a combination of skill and luck. (as most games are). We assume that if the game was all luck and/or we all had the same skill level eventually the ...
5
votes
2answers
161 views
Distribution of ratio of sample means from two independent normal variables?
The Question
We have a sample of size $N$ with mean $\bar{x}$ and SD $\bar{\sigma_x}$ from a random variable $X \sim \mathcal{N} (\mu, \sigma^2)$
We have a sample of size $M$ with mean $\bar{y}$ and ...
4
votes
1answer
67 views
High dimensional parametric skew distribution
What are the best researched options for a parametric multivariate probability distribution that is able to be skewed, given curvature, and possibly even multiple modes? I have done some research into ...
3
votes
3answers
220 views
How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
I stumbled upon the following problem:
Given 'n' dice with 'm' faces with values 1 to m and a number 'x' what is the probability that the sum of the numbers on the 'm' dice is greater than or equal ...
0
votes
0answers
32 views
Objective automatic method of estimating tail index
I'm looking for a practical, objective method of tail index estimation.
So far I have found this working paper An Automatic Procedure for the Estimation of the Tail Index. Since it has not been peer ...
1
vote
1answer
101 views
Bayesian updating - which distribution to use
I'd like to use Bayesian updating to form price expectations to be used in another model. I'm very new to this area, so your help would be highly appreciated.
I'm not sure which distribution to use ...
6
votes
1answer
137 views
Replicating simulation results from a paper
I’m reading R. Kreps' paper Parameter uncertainty in (log)normal distributions and trying to figure out how the simulations were done. In order to generate Figure 1, Eqn (2.41) was used. So this is ...
2
votes
0answers
113 views
Combining posterior distributions
I have 5 different posterior distributions (mcmc samples) which all estimate the same parameter beta. The 5 models are all obtained from 5 independent standardized datasets but estimate the same ...
5
votes
1answer
76 views
Elementary approach to higher order asymptotics
I am trying to understand “higher order asymptotics”. I find several texts on Likelihood asymptotics, nothing’s easy to read... if you have any nice pointers on this direction, I’ll be interested; ...
0
votes
0answers
38 views
Distribution of transformation
Suppose $X_1,\ldots,X_n$ are i.i.d. $\mathcal U(0,1)$. I am looking for the asymptotic distribution of $$T_n = \prod_{i=1}^n [e{X_i}]^{1/\sqrt{n}} \>.$$
10
votes
2answers
241 views
What's the name of this discrete distribution (recursive difference equation) I derived?
I came across this distribution in a computer game and wanted to learn more about its behaviour. It comes from the decision as to whether a certain event should occur after a given number of player ...
7
votes
2answers
215 views
Simple question about the asymptotics of estimators
Consider any arbitrary estimator called $\hat{M}$ (e.g., regression coefficient estimator or specific type of correlation estimator, etc) that satisfies the following asymptotic property:
...
0
votes
0answers
88 views
Tail distribution of sum of weibulls
Is the any nice bound on tail distribution of a finite sum of i.i.d weibull random variables?
1
vote
1answer
428 views
Fitting t-distribution in R: scaling parameter
How do I fit the parameters of a t-distribution, i.e. the parameters corresponding to the 'mean' and 'standard deviation' of a normal distribution. I assume they are called 'mean' and 'scaling/degrees ...
0
votes
1answer
101 views
Building a summary for values drawn from a bimodal distribution
I have a statistic that assign values to categories of products. This statistic shows strong bimodality (see graph).
For analysis, I am trying to assign a value of that statistic to each product ...
2
votes
1answer
99 views
How can I identify probability mass functions with known proportions of contribution in a series of histograms?
Suppose I have two real-valued PMFs $f(i)$ and $g(i)$ with $1\le i\le N$ and $N$ is about 1 billion. The functions $f$ and $g$ can be assumed to be continuous on the positive integers, one-sidedly so ...
1
vote
0answers
21 views
Relative to a Population: Statistically Valid Method for Categorizing Something as “Other”?
I am working similarity searching of an HTTP Request relative to the last N number of days of requests my system has collected using locality sensitive hashing based on Moses Charikar's "Similarity ...
1
vote
2answers
196 views
Distribution of number of Bernoulli trials given number of successes
Suppose you have a series of n trials, where the probability of success
in each trial is p. The distribution of the number of successful trials
follows a Binomial distribution with parameters (n, ...
1
vote
1answer
25 views
Suitable distributions for the SDs of a number of groups (or participants)?
When analyzing data, using MLE or Bayesian methods, one needs to assume a distribution for the data. For continuous data the are a number of distributions that are often considered, for example, the ...
1
vote
1answer
98 views
Modeling Outliers of Normal Distribtuion
I am using a linear model to predict under-nutrition in children under 5. The common metric discussed is stunting (a binary outcome) which is defined as being more than two standard deviations away ...
8
votes
3answers
326 views
Parameter estimation of exponential distribution with biased sampling
I want to calculate the parameter $\lambda$ of the exponential distribution $e^{-\lambda x}$ from a sample population taken out of this distribution under biased conditions. As far as I know, for a ...
0
votes
3answers
105 views
What are the rules for picking a distribution for modelling a data set?
I have a data set of 100,000+ event times. For this study an event begins (at time 0) and can run for an indeterminate amount of time. The bulk of events require a couple of hours to complete but ...
1
vote
0answers
94 views
computing slope on heavy tailed lognormal distribution
I have a heavy tailed logNormal distribution and i want to know if it's possible to make a linear regression in order to compute R² and slope for this data.
I make my linear regression on computed ...
1
vote
0answers
90 views
What does weighted cumulative frequency distribution mean?
I have two sets of data (temperature and catch) and I am following a proposed method in an article I am reading on the empirical cumulative function (ECDF) analysis. Firstly, I have derived the ECDF ...
1
vote
0answers
37 views
General distributions for which binomial and Poisson are special cases
I have an unknown discrete distribution $f(x; a,b,c,d)$. Of the 4 parameters one is redundant. I have found some limiting cases:
$$X\sim\text{Binomial}(g(a,b,c,d),c/(b+c)))\;\;\; b,c \gg a,b$$
...
1
vote
2answers
161 views
Topic Words Selection in Topic Modeling
I understand how generative model of topic modeling works; for each topic there is a distribution of words, and for each document there is a distribution of topics.
Question is how words are ...
0
votes
0answers
65 views
Working with an arbitrary number of sample moments
The $n^{th}$ moment of a distribution can be estimated from a vector of samples $(x_1,x_2,...x_k)$ by:
$$
\sum_{i=1}^{k} x_i^n
$$
Now, let's say I've calculated the first $m$ moments for my ...
1
vote
1answer
66 views
Variance of compound distributions
I am stuck at solving analytically the variance (or standard deviation) of a combination of poisson distribution and Beta-Distribution (or more exactly, PERT distribution). The background is that for ...
1
vote
0answers
20 views
The statistical prevalence of solely negative genes in the adult human population?
I really hope I'm not asking this question on the wrong stackexchange site, but seen as this question has a lot to do with statistics I'm guessing I might be in the right place.
There are certain ...
3
votes
1answer
165 views
Sum of Binomial and Poisson random variables
If we have two independent random variables $X_1 \sim \mathrm{Binom}(n,p)$ and $X_2 \sim \mathrm{Pois}(\lambda)$, what is the probability mass function of $X_1 + X_2$?
NB This is not homework for ...
1
vote
4answers
365 views
Predicting the outcome of the next coin toss?
Tossing a fair coin is i.i.d. Let's assume that I have that:
Coin = {H,H,H,T,T}
How would you guess the next coin and why?
PS: I looked for Bernoulli ...
2
votes
2answers
141 views
What's the resulting distribution when you take the N times self convolution of normal(mu, sigma) where N~Poisson or binomial
So if you have $N \sim \mathrm{Poisson}(\lambda)$ or $N \sim \mathrm{Binomial}(n,p)$ I'm curious about the convolution $$X = \sum_{i=1}^N X_i$$
(where $X_i \sim \mathrm{Normal}(\mu, \sigma)$ and $X=0$ ...
