# Tagged Questions

20 views

### Estimating the distribution from partially aggregated data

I have a dataset that consists of a list of tuples: (1, .5), (3, .7), (1,.1), (23,.8),... In each tuple, the second element is the average price, and the first ...
34 views

### How to estimate a pdf of x under the model of y = x+n, when the pdf of y and the pdf of n are given

I guess I come up with a classic question, but I failed to find any useful solutions by far. My question is about the following model $$y=x+n$$ where $x$ is a hidden random variable that cannot be ...
37 views

### How to get exact distribution of estimated p for binomial distribution?

This question is kind of a follow up of another question I had: Asymptotic normal distribution via the central limit theorem There I had to calculate the estimator for $p$ (meaning $p$ for success) ...
61 views

### Estimating of point in the density of bimodal distribution

I'm trying to estimate a specific point in a bimodal distributions, It's the point that I indicated in my picture with the A. As example we can generate a mixture of guassian and then try to ...
160 views

### Usable estimators for parameters in Gumbel distribution

The Gumbel distribution has the general form: $$F(y)=\exp\left({-\exp{\left(-\frac{y-\mu}{\sigma}\right)}}\right), \quad y\in \mathbb{R}$$ where $\mu \in \mathbb{R}$ and $\sigma >0$. Let ...
216 views

### Fitting data in a generalized Pareto distribution and parameter estimation

I have log(return) data as time series, how I can fit this data in a Generalized Pareto distribution and estimate the parameters of this distribution, any kind of resource pointer with clear code ...
57 views

### 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 ...
96 views

### Estimating a distribution from above/below observations

Let $P$ be an unknown distribution on $(-\infty,\infty)$. Let $X_1,\ldots,X_n$ be an iid sample from $P$. Let $c_1,\ldots,c_n\in(-\infty,\infty)$ be a known set of constants. We observe ...
45 views

### The meaning of translation completeness w.r.t a random variable

I stumbled upon this term in McFadden - Analysis of qualitative choice behavior (page 111). It is said that "A random Variable $X$ is translation complete if for a function h of bounded ...
50 views

### Bias in EM estimation for a mixture of normal distributions

Are the parameter estimates for a mixture of two normal distribution using EM algorithm biased or unbiased? More specifically, if I use the EM-algorithm to obtain ML estimates of $μ_1$, $μ_2$, ...
114 views

### Gaussian vs non-gaussian distribution

Let we have data of 3D (example angular velocity x, angular velocity y, angular velocity z).Can anyone explain/give example/how to differentiate between gaussian distribution and non-gaussian ...
52 views

### How to estimate a distribution?

Suppose I have estimated the discrete income distribution for Maryland, and the average distribution for the U.S. What is the algorithm or method to estimate the income distribution for Pennsylvania, ...
278 views

### Robust parameter estimation for shifted log normal distribution

I have a data set which fits a logNormal distribution quite well. (From a theoretical point of view, it is some hard-to-tackle quotient distribution). However, the data is quite dirty, so parameter ...
195 views

### Robust parameter estimation for Exponentially modified Gaussian distribution

I'd like to test how well my data can be modeled by an Exponentially modified Gaussian distribution (Wikipedia) or Normal-exponential-gamma (NEG) Distribution. However, the parameter estimation (which ...
835 views

### Maximum likelihood estimators for a truncated distribution

Consider $N$ independent samples $S$ obtained from a random variable $X$ that is assumed to follow a truncated distribution (e.g. a truncated normal distribution) of known (finite) minimum and maximum ...
136 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 ...
461 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 ...
96 views

### Long-tailed distribution of time events

Suppose you have the logs of a web server. In these logs you have tuples of this kind: ...
162 views

### What practical application is there for the Asymptotic Mean Integrated Squared Error in kernel density estimation?

Introduction For some time now I have been struggling to understand how theoretical results can be applied in practice. Fortunately in most cases the link between theory and practice is not hard to ...
126 views

### Rank-ordered cumulative distribution estimation: where does this function come from?

I am reading over some process analysis data for some failure analysis tests, and I have come across the following definition of an "estimated cumulative probability": $$F(t) = \frac{i-3/8}{N+1/4},$$ ...
364 views

### Estimating the parameters of a beta distribution with zeroes and ones in the sample

I have a list of values in [0,1] that I want to fit to a Beta distribution in order to get the corresponding alpha parameter. I can't use a beta fitting function because my values might be 0's and ...
206 views

### How to estimate storage needs using the PERT distribution for filesizes? How to aggregate them without falling into the flaw of extremes?

Lets say I know that I am going to store the information of 10,000 people each year for 4 years, that is 40,000 files. Now If I estimate that on the best case scenario the information from each ...
209 views

### Estimating the parameters of a sum of a Gaussian and an $\alpha$-stable random variable

Let's assume I have a set of samples of a random variable $$X = Y + Z \>,$$ where $Y$ is Gaussian (with a mean of zero and variance $\sigma^2$) and $Z$ has a symmetric $\alpha$-stable ...
150 views

### Confidence Band for Probability Mass or Density Function

I'm a beginner -- don't hesitate to overexplain. I need to make inferences about a population distribution from a sample distribution of a continuous variable (which is still useful as an ordinal ...
849 views

### Variance-gamma distribution: parameter estimation

I have quite a general question about Variance-gamma distribution. I am interested in how to estimate it's parameters given a set of training points? I tried to find the answer in the internet, but ...
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### Scaling of huge data and estimating the distribution

Suppose you have some sample of huge numbers and you want to fit some continuous distribution to these numbers. You will get some distribution that is loosely speaking highly "smeared", e.g. it has a ...
196 views

### Expectation of an estimator?

When evaluating an estimator in a frequentist setting, using MSE and let say to compute the Bias of the estimator we compute the expectation of this estimator, are we supposing that the estimator has ...
208 views

### Mathematica SmoothKernelDistribution equivalent in R

@vucko gave me excellent answer on my question, unfortunately using Mathematica code. I'm trying to rewrite it in R and I'm lost in R functions providing kernel density estimation. I have bivariate ...
79 views

### Appropriate sample statistics to provide a reliable estimator for an Erlang-like parent population

We would like to measure (in near real-time) the completion latency of requests to our queue-based system. The volume of inbound requests is sufficiently high that we would like to sample/aggregate ...
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### Estimating joint distributions using copula package in R

I am trying to estimate the joint distribution of stock returns using the copula package. I have read a couple of papers on copulae, but alas my lack of math ...
363 views

### Estimating kappa of von Mises distribution

Is there a way to calculate an estimate of $\kappa$ from data for the von Mises distribution? It seems very easy to do in R, http://rgm2.lab.nig.ac.jp/RGM2/func.php?rd_id=CircStats:A1inv, but python ...
101 views

### Guessing the appropriate 'distribution' of an observation to perform some form of sensitivity analysis

I wish to run some simulations on the 'estimates' of an event provided by experts (or historical data if available). For example: The technology manager of company X says that probably 300-1000 ...
129 views

### Estimate non-parametric prediction interval

Maybe let me first describe the real world application of my problem before going to a more mathematical model. Suppose I have a system that measures my current position up to an unknown error (let's ...
295 views

### Which is a good tool to compute parameters for a beta-distribution?

I have a β-distribution(which looks like a normal distribution), for which I want to calculate the values of α and β using maximum likelihood estimation method. I am new to statistics, so would like ...
94 views

### calculate the rate of change

I posted this on maths, but seems it would be better here :S http://math.stackexchange.com/questions/49941/calculate-the-rate-of-change Basically I am trying to calculate the change frequency for ...
10k views

### Calculating the parameters of a Beta distribution using the mean and variance

How can I calculate the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the mean and variance that I want the distribution to have? Examples of an R command to do this would be most ...
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### Estimating the distribution of a very large population of known size and unknown variance

I would like to estimate the distribution of a very large population of known size but unknown mean and variance. I cannot assume anything about the shape of the underlying distribution. However, I ...
520 views

### What kind of distribution is $f_X(x) = 2 \lambda \pi x e^{-\lambda \pi x ^2}$?

What kind of function is: $f_X(x) = 2 \lambda \pi x e^{-\lambda \pi x ^2}$ Is this a common distribution? I am trying to find a confidence interval of $\lambda$ using the estimator ...
94 views

### Using an OLS coefficient to estimate a non-linear coefficient

Using OLS, I've estimated the following equation: $y_i = \alpha_0 + \alpha_1 X_i + \epsilon_i$ I know that theoretically, the following should be true: $y_i = a + (1-e^{-\lambda 60}) X_i$ Is ...
1k views

### How to estimate parameters for Zipf truncated distribution from a data sample?

I have a problem with the estimation parameter for Zipf. My situation is the following: I have a sample set (measured from an experiment that generates calls that should follow a Zipf distribution). ...
3k views

### How to calculate Zipf's law coefficient from a set of top frequencies?

I have several query frequencies, and I need to estimate the coefficient of Zipf's law. These are the top frequencies: ...
370 views

### Get distribution curve characteristics by selecting peak point?

I have no math or stats background, so this may be a real dumbo question. I'm developing a time estimation app which would let user enter her worst case and best case estimates, and then select a ...
532 views

### Kernel density estimate takes values larger than 1

I am using scipy.stats.gaussian_kde to estimate a pdf for some data. The problem is that the resulting pdf takes values larger than 1. As far as I understand, this ...
419 views

### How to check that a sample suits multi-dimensional uniform distribution?

I have a 3-dimensional sample $(X_k,Y_k,Z_k), k=1, \ldots, N$ which I suspect to be uniform on some parallelepiped in $R^3$ (i.e. a set of the form [a;b]X[c;d]X[e;f], where numbers a,b,c,d,e,f are ...
One of the purported uses of L-estimators is the ability to 'robustly' estimate the parameters of a random variable drawn from a given class. One of the downsides of using Levy $\alpha$-stable ...