1
vote
1answer
89 views

Physical significance of heavy tail distributions

I have come across several usage of the term "heavy tail distributions", but unable to find some good resources in the Internet to answer few of my questions: Compared to what the tail of the ...
0
votes
0answers
16 views

Why is the CDF of the maximum of two random variables their respective CDF's multiplied? [duplicate]

I have the following random variables: X = uniform over [0, 1] Y = uniform over [0, 1] Z = max{X, Y} (X and Y are independent) I don't understand why the CDF of ...
1
vote
1answer
46 views

Finding moments for a theoretical density function

I am working on finding higher order moments for a given theoretical function, to be used in modelling of daily log-returns. The PDF is, $f_r(x) =$ $\begin{cases} \quad ...
5
votes
1answer
67 views

Measure of dispersion over unordered set

I'm looking for a measure of dispersion, such as standard deviation, that can be used when distributing to an unordered set. Specifically: A bucket distribution assigns a non-negative value to each ...
0
votes
0answers
64 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
0answers
82 views

Is there a name for these kinds of graphs?

I am just wondering - is there a name for these kinds of graphs? The associated text that comes with the graph says the following: Figure 2 presents a view of the distribution of correctable ...
1
vote
0answers
344 views

What is the physical meaning of the probability density function and cumulative distribution function?

I have started research in Electronic Engineering, where PDF & CDF take a core part in most of the applications. I have studied books on probability where they have discussed the PDF & CDF ...
3
votes
1answer
337 views

Kolmogorov-Smirnov Test Alternatives

I'm comparing 2 data sets from nearby locations to see if they differ significantly in air quality. I cannot perform any paired tests because the data at one location does not necessarily correspond ...
8
votes
0answers
257 views

Gaussian Ratio Distribution: Derivatives wrt underlying $\mu$'s and $\sigma^2$s

I'm working with two independent normal distributions $X$ and $Y$, with means $\mu_x$ and $\mu_y$ and variances $\sigma^2_x$ and $\sigma^2_y$. I'm interested in the distribution of their ratio ...
6
votes
1answer
2k views

How to calculate cumulative distribution in R?

I need to calculate the cumulative distribution function of a data sample. Is there something similar to hist() in R that measure the cumulative density function? I have tries ecdf() but i can't ...
0
votes
1answer
608 views

How to find the inverse of non-standard CDF in Matlab?

The cumulative distribution function (CDF) for a truncated log-normal distribution is represented as shown below. How can I find its inverse in Matlab? ...
3
votes
1answer
924 views

Distribution of a ratio of uniforms: What is wrong?

Suppose that $X$ and $Y$ are two i.i.d. uniform random variables on the interval $[0,1]$ Let $Z=X/Y$, I am finding the cdf of $Z$, i.e. $ \Pr(Z\leq z) $. Now, I came up with two ways of doing this. ...
3
votes
1answer
513 views

Can a negative binomial distribution be used to model a continuous distribution?

I have a data set which is a set of continuous distances from some origin. I originally modeled this as a negative binomial distribution by rounding the data and using it as an input in the Matlab ...
2
votes
1answer
275 views

Calculating event probabilities in mixed, discrete/continuous distributions

This is a simple question. I am dealing with a "clipped" normal distribution -- say, $N(0,0.5)$ clipped between $[-1,1]$. I would like to calculate the "probability" of a sample, but I know that in ...
3
votes
1answer
253 views

What is the closed form solution for the inverse CDF for Epanechnikov

Is there a closed form solution for this inverse CDF?
6
votes
2answers
1k views

Use Empirical CDF vs Distribution CDF?

NOTE: I purposely did not label the axis due to pending publications. The line colors represent the same data in all three plots. I fitted my data using a negative binomial distribution to generate a ...
3
votes
2answers
157 views

Efficient Empirical CDF Computation / Storage

I'm trying to precompute the distributions of several random variables. In particular, these random variables are the results of functions evaluated at locations in a genome, so there will be on the ...
7
votes
2answers
3k views

Finding the PDF given the CDF

How can I find the PDF (probability density function) of a distribution given the CDF (cumulative distribution function)?