8
votes
0answers
97 views

Product of two independent random variables

I have a sample of about 1000 values​​. These data are obtained from the product of two independent random variables $\xi \ast \psi $. The first random variable has a uniform distribution $\xi \sim ...
1
vote
1answer
56 views

How to estimate true value and 95% bands when distribution is asymmetrical?

I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
5
votes
2answers
80 views

Distribution for number of trials before a fixed sum is reached

I'm trying to figure out the distribution over a number of trials until a stopping condition is met. In particular, imagine we are observing samples of a uniformly distributed random variable, $X \in ...
3
votes
2answers
81 views

Is there a smooth probability density function with finite moments and a closed form quantile function?

I am looking for a smooth probability density function with finite moments and closed form quantile function. As one knows, an example of smooth probability density function with finite moments is the ...
1
vote
2answers
78 views

Can any probability distribution be written as a Boltzmann distribution?

By redefining the energy function, $E(x)$, can any $p(x)$, be written as a boltzmann distribution, ie. $p(x) = \frac{e^{-E(x)}}{Z}$, where Z is the partition function?
0
votes
1answer
55 views

Determining butterfly weight distribution

I'm a researcher studying a specific butterfly species. I've conducted an experiment where I measure the weight of this species at different locations on the earth. The data is cateogorical and ...
0
votes
1answer
36 views

Cumulative Distribution Function

If I need to determine the value of a data point at each percentile of a distribution (such as lognormal, weibull, etc), can use its CDF and plug in %iles to get the value? For e.g. finding the value ...
0
votes
0answers
42 views

Determining sample size in a non-normaly distributed data

I want to take some samples from a database nearly ~150.000 records of a non-normally distributed values. From this link I obtained some common procedures to find a sample, influenced by The level of ...
0
votes
1answer
47 views

Comparing two points corresponding to two different normal distributions

I have two multi variate normal distributions N1 and N2. Say two points p1 is from N1 and p2 is from N2. I want to get some statistical features from these two points. How can I do it? I need a ...
0
votes
2answers
69 views

Normal approximation to binomial

What do I do when the normal approximation is not valid? Here's the question I'm trying to answer: A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
0
votes
1answer
63 views

Cumulative function to probability density function

I have some data points for which I would like to show the density using Python, but the package SciPy is not working for Python 3.3. I am looking for a solution to be able to plot some data in the ...
1
vote
1answer
61 views

Probability distribution to simulate number of users

I need to simulate with probability distribution number of users who are listening radio during the day. Given data : max number of users is 1000, day has 24 hours (from 0 to 24), the highest number ...
0
votes
0answers
80 views

Uniform Random on $(-\infty,\infty)$

Imagine picking a 1 when any real number is equally likely. What is the pdf? Does this idea have a known use? What is its name? There could be a use for a uniform random real number. It could end ...
0
votes
1answer
81 views

What is the 'same distribution' mean?

Say if I have two random variable X and Y and they have the same distribution, what is that suppose to mean? Is that mean they have same mean and variance?
0
votes
1answer
47 views

Identify lazy grading from distribution of test scores?

For the end-terms in a large public university (LPU), there were qualitative tests for 5 courses. Every one of the 1000 students took every test, so there are 5000 answer scripts. Every test was ...
3
votes
0answers
58 views

Distribution of variable

How to find the distribution of $$\sum_{i=1}^n (X_i - X_{1:n}),$$ where $X_i$ are i.i.d. random variables and $X_{1:n} = \min(X_1,X_2,...,X_n)$? I need to find the distribution in a particular case, ...
1
vote
3answers
109 views

Discretizing Exponential distribution

I am working on a packet generator that can generate packets of 50 different sizes and the packet sizes follow exponential distribution. Given a mean packet size how can I choose the 50 packet sizes ...
2
votes
0answers
104 views

Kullback-Leibler vs Hellinger Distance

I am working on this problem in which I have a dataset of n-dimensional examples that come from different and unknown distributions. Given a new sample, I wish to find k examples from the dataset that ...
5
votes
1answer
89 views

Kernel density estimation on asymmetric distributions

Let $\{s_1,\ldots,s_N\}$ be a set of samples drawn from an unknown (but certainly asymmetric) probability distribution. I would like to find the probability distribution by using the KDE approach: $$ ...
2
votes
1answer
55 views

description of a Wiener Process assuming a Laplace Distribution

Is there a description of the Wiener Process when a Laplace distribution is assumed rather than a normal one?
0
votes
2answers
151 views

Recommendations for learning probability and Bayesian statistics? [duplicate]

I have been very interested lately in learning Bayesian Statistics, but I have only a little bit of background in the frequentist statistics, only one term at University. Some of the books that I ...
2
votes
0answers
67 views

Distributions similar to the family of stable distributions

Are there any other distributions with similar properties to the family of stable distributions? That is, $\alpha$-stable, normal tempered stable, classical tempered stable, etc. etc. where the ...
2
votes
1answer
54 views

Probability distribution for varying probabilities in R

I'd like to plot the probability distribution for a set of binomial trials in R, the catch is that each trial has an independent probability of success (which I have in vector form). So, in R if I ...
1
vote
2answers
181 views

Importance of normal distribution

Why did the normal distribution become such a popular (important) distribution? I know one reason is because of CLT. Can you please give more reasons?
4
votes
1answer
68 views

Urn with non-uniform probabilities

An urn contains N-1 red and 1 green ball. Each ball has an associated weight. If each ball is drawn (without replacement) with a probability proportional to how much its weight contributes to the urn, ...
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
votes
2answers
211 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.
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 ...
3
votes
3answers
221 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 ...
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 ...
1
vote
2answers
197 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
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
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 ...
1
vote
0answers
30 views

Sampling distributions help with questions [duplicate]

Possible Duplicate: Probability of mean of random sample being in a certain range When a pizza restaurant’s delivery process is operating effectively, pizzas are delivered in an average of ...
0
votes
1answer
113 views

prior distribution to the binomial distribution probability distributions urn model

I have an infinite population with unknown mean of successes and failures. I'm drawing 400 times from the population and get 400 successes. Now I want to generate random estimates for the true mean of ...
3
votes
1answer
147 views

Tail bounds on a function of normally distributed variables

I am looking for tail bounds (both at $0$ and at $\infty$) for $$ Z:=\exp \left(\frac{\alpha}{4}(X-Y)^2+\frac{\alpha}{2}(X+Y)\right)$$ where $\alpha$ is a positive real and $X,Y$ are i.i.d. normal ...
0
votes
0answers
91 views

Deriving asymptotic distribution

I'm working on a question and I appreciate if you could guide me on how to approach it. Here is the question: Consider $Y_1, Y_2, \ldots, Y_n$ as iid with density $f(y;\theta)$ and assume that the ...
1
vote
1answer
46 views

Does any one know what is the P value when F=37.45; df1=5; df2=40 in a one way anova F test?

in a one way anova F test when F=37.45; df1=5; df2=40 what is the P value? I tried several software, and the result is <0.0001. I know it sounds weird that I need a really small number of ...
2
votes
0answers
64 views

Modeling a 1D random walk with nonconstant probability in a point

There is a 1D discrete random walk system which the probability of all points are 1/2(probability of going forward and backward) except one point which locate on l (l is an integer number).the ...
2
votes
1answer
83 views

How to produce a vector based on two probability distributions?

I am working on distribution on plants and I need to enter the chances that a plant starts reproducing at a certain age in a vector. Only this has to be done for more generations. Now, Imagine I ...
4
votes
2answers
96 views

Which probability distribution function applies to my problem?

OK the problem came from an AI course that I attended this year. You can find the problem description here In short we have a number of birds in the sky that we need to shoot down. In the main ...
7
votes
3answers
458 views

Measure the uniformity of distribution of points in a 2D square

I have a 2D square, and I have a set of points inside it, say, 1000 points. I need a way to see if the distribution of points inside the square are spread out (or more or less uniformly distributed) ...
-1
votes
3answers
472 views

The meaning of P(X=0) in a binomial distribution

recently I was resolving an elementary problem about binomial distribution, this problem requests to determinate $P(X<=2)$, where $X$ is nonconforming products, sample is 50 units, and the fraction ...
0
votes
1answer
33 views

Finding anomalies in industrial part failures

I have a data set that is composed of the age an industrial machine part is when it fails (x variable) and the part's width in nanometers (y variable) at the time when it fails. The data looks ...
3
votes
1answer
156 views

How to generate a probability of x given a value of y and a distribution?

I have a bivariate data set where x and y values, both continuous variables, correlate well (visually speaking) when x and y are small. As the values of x and y increase, the correlation decreases to ...
4
votes
1answer
163 views

Inequality for bivariate normal distribution

Let $X_1$ and $X_2$ be bivariate normal with mean $\mu=(0,\mu_2)$, for any $\mu_2$, and correlation $\rho$. Consider the following inequality: \begin{align*} Pr\left\{|X_1| \ge ...
3
votes
1answer
173 views

Order statistics of absolute value of bivariate normal distribution

Suppose $X_1$ and $X_2$ are bivariate normal and let $|X|_{(1)}$ and $|X|_{(2)}$ be the ordered version of their absolute value. I am interesting in finding the following probabilities or some bounds ...
2
votes
1answer
61 views

Modeling nearest event through multivariate random variable with condition

There are two time sequences in my system, one of them represents IN events, and the other OUT events. Each IN event would be released by the nearest following OUT event or reaching the deadline. I ...
1
vote
0answers
73 views

Question related to binomial distribution

Let $X \sim Binomial (n, p)$ with both $n$ and $p$ known. Suppose for some non-increasing function $G:[0,1] \rightarrow [0,1]$, and some fixed $c_0 \in [0,1]$, we have that \begin{align} ...

1 2 3