Questions on the use of mathematical techniques to extract properties from given data. Consider if your question might be more suited for Cross Validated (stats.SE) instead.

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Type 2 Error Question - How to calculate for a two tailed?

The modulus of rupture (MOR) for a particular grade of pencil lead is known to have a standard deviation of 250 psi. Process standards call for a target value of 6500 psi for the true mean MOR. For ...
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19 views

Confidence Interval Question - How to verify using CDF, PDF?

Question: Use the distribution of U to verify that P((α/2)^1/n ≤ Y/θ ≤ (1 − α/2)^1/n) = 1 − α. Derive a 100(1 − α)% confidence interval for θ based on this probability statement. I have calculated ...
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1answer
33 views

How to prove MLE of theta is unbiased?

Let $X_1, X_2, . . . , X_n$ be a random sample from a uniform distribution on $[0, \theta]$. Suppose results $x_1, x_2, . . . , x_n$ are observed. Since $f(x) = 1/\theta$ for $0 \leq x \leq \theta$, ...
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1answer
32 views

Uniform Distribution Question - Help Needed

Let $X_1, X_2, . . . , X_n$ be a random sample from a uniform distribution on $[0, \theta]$. Suppose results $x_1, x_2, . . . , x_n$ are observed. Since $f(x) = 1/\theta$ for $0 \leq x \leq \theta$, ...
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22 views

Numerical Analysis Stability or Condition

Im not sure if its the right place to ask this question since it may be more of an informatics problem and I apologize if its the case: I want to evaluate a certain function, $\frac{log(cos(x))}{x}$ ...
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1answer
27 views

Conditional Probability of a group of Mice

There are six female and four male mice in a group of 10. One of the female mice and two of the male mice have a particular disease. Suppose that two mice are selected at random from the group without ...
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0answers
14 views

Fourier transform used for time series prediction?

For a given time series data set $(t=0,...T)$, we can use Fourier transform to data fitness $$ X(n) = \mu + \sum_{k}\left( A_k cos \frac{2\pi k n}{N} + B_k cos \frac{2\pi k n}{N} \right) +\varepsilon ...
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1answer
16 views

Predicting values based on given data

num value 8 ? 10 ? 12 24.33 16 22.5 20 22.29 24 22.41 28 22.55 32 ? 36 ? let's say i have the following ...
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1answer
984 views

Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
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0answers
17 views

Can I use the dispersion index for a variable that is NOT normally distributed?

If I have a variable graphed as a function of time, that is not normally distributed, does it make sense to use its (time-varying) dispersion index, $\mathrm{Var}(x)/E(x)$ to compare its volatility ...
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3 views

Show that the maximum of a function is achieved in one of the data

I'm new to data analysis, and started working with circular data. Let $t_1,\dots,t_n\in [0,2\pi\rangle$. If we want to find the representative of the data on the unit circle, we must maximize the ...
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5answers
357 views

Finding the orientation of a noisy ellipse

This question comes from a neuroscience study which generates $12$ vectors. The vectors are evenly spaced, $30 n$ degrees for $n=0,\dots, 11$, each with their tail centered on the origin. I am ...
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0answers
20 views

Relationship between eigenvectors of correlation and covariance matrices

For the purpose of computing principal components of a dataset, represented as matrix $X$ of dimensions $n \times p$ with $n$ samples and $p$ features, we can compute sample covariance matrix $S$, and ...
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0answers
9 views

Understanding the bound given by Johnson–Lindenstrauss lemma

Here I choose to use the statement made by S.Dasgupta: For any $0<\epsilon<1$ and any integer $n$, let $k$ be a positive integer s.t. $$k \geq 4(\epsilon^2/2-\epsilon^3/3)^{-1} \ln n $$ Then ...
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0answers
12 views

Curve fitting: How to identify the appropriate function for a beat-like phenomena?

I have a time series data which shows some beat like behaviour. The envelope does not look exponentially decreasing, as it is impossible from a physics point of view. The envelope is likely to be a ...
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0answers
10 views

Getting a feel for the Normal-Inverse-Wishart conjugate prior to multivariate normal distribution

I am trying to get a feel for the Normal-Inverse-Wishart conjugate prior, which I have started to use, sparingly, in my work, where I am trying to cluster multivariate normal data. As Wikipedia ...
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0answers
23 views

Spectral relaxation of k-means clustering

I am working on a presentation on Spectral relaxation of k-means clustering (http://papers.nips.cc/paper/1992-spectral-relaxation-for-k-means-clustering.pdf) and I am a bit stuck. I understand ...
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1answer
31 views

Tropical geometry: practical applications?

In 1960, E. Wigner published a paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Theoretical mathematical structures pave the way to further advances and ...
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0answers
16 views

What is trend analysing

Hi I'm just started learning DFA for stochastic processes and I faced to the "trend".I've looked around the internet about trend analysing but still I don't understand it completely.can you define ...
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1answer
17 views

Alternatives to Shephard interpolation?

I am a chemist, so I have little experience in the field of math. My program is that I have a set of points (approx. 20000) in some larger dimensional space (like 10-20 dimensions), and I want to be ...
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2answers
27 views

How can I determine the best relationship for 3 variables, given several data points?

What is the best way to determine the relationship for three apparently related variables? The relationship does not appear to be linear, and may follow a combination of non-linear functions. I have ...
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0answers
12 views

likelihood function when data and model share a common parameter

I'm having some conceptual difficulty with how to describe, and deal with, a problem related to constructing a likelihood function that will be used to fit a model to data. Sorry in advance if I ...
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1answer
26 views

How to prove convergence of a sequence maximizing a sum of exponential distances?

I want to find the argument $x$ that maximizes $f(x)=\sum_i e^{-(x-d_i)^2/c}$ for some data values $d_i$ and an arbitrary positive constant $c$. I assume that $f(x)$ has only a single maximum (most ...
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30 views

Random walk in high dimensional space with stationarity

I have a vector of high dimension ( say 100). When I take a random walk ( i.e add a step value to each components of the vector, the step value being drawn randomly drawn from standard normal ...
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0answers
10 views

Minimal sufficient statistics for log-multiplicative/log-nonlinear models

I am interested in minimal sufficient statistics of Association models for variables for ordered categories developed by Goodman (http://doi.org/10.2307/2287833). In particular, consider an $I\times ...
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16 views

Number of clusters in $k$-means clustering for higher-dimensional data.

I've read the Wikipedia article and a lot of posts on stackexchange (like this really thorough one) on determining the number of clusters in a data set. Based on that, I am currently using the ...
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0answers
16 views

Calculate the difference of binary vectors

I have a matrix with 579 columns (points of data) and 138 rows (objects I am comparing). The points of data is binary - either it matches or it doesn't match. I am working under the assumption that ...
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1answer
33 views

Proving relations between square cosines

I am studying data analysis and especially PCA (principal component analysis) and reviewing the very course i took a few years ago, i found a result that seems interesting but there is no proof and i ...
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0answers
19 views

Setting up Vandermonde matrix with data points containing derivatives

I know how to setup the Vandermonde matrix with simple interpolation conditions, such as p(-1)=4 p(0)=7 p(1)=28 p(2)=247, i.e. (-1,4),(0,7),(1,28),(2,247) ...
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0answers
4 views

Q-Q plot of R.V with normal distribution and R.V with negatively skewed distribution

I wonder the shape of the Q-Q plot of R.V with normal distribution and R.V with negatively skewed distribution. I want to know how the graph looks like, and more importantly, why it would be. ...
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0answers
10 views

Coalitional effect in logistic regression and assessing explanarory variable contribution

I have a problem that could be described as logistic regression with all dichotomous variables: 1 response variable (DV) Y (I would call it later as a feature/violet star) and 5 explanatory variables ...
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2answers
81 views

Outlier detection with robust multiple regression model

I have a set of features (eg, location, income, budget, education) that I use to predict a continuous variable (say, amount spent per day on the internet). I am interested in detecting outliers. I ...
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2answers
58 views

Approximating statistics for huge dataset

I'm investigating users accounts statistics for Vkontakte social network. There are $N\approx2 \cdot 10^8$ accounts that have different metrics along them – boolean, discrete and continuous. I found ...
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2answers
27 views

Is this histogram considered bimodal?

Is this histogram bimodal? Because when I google what a bimodal histogram looks like, I keep getting images that say histograms like these are considered bimodal. Isn't it unimodal because the ...
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4answers
48 views

What is the purpose of finding a model to best fit data?

So given the following question: What is the purpose of finding a model to best fit data? Someone answers: The purpose of fitting data to a curve is so that you can give an exact statement about ...
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1answer
23 views

Can I apply a one-way ANOVA and Tukey test to this data?

The experiment: Effect of pH on yeast respiration. I tested 5 different pH levels and measured the amount of CO2 produced. The data shows a trend similar to upside down parabola. Would it make sense ...
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2answers
49 views

Inversion of the Burrows Wheelers Transform

The "Burrows-Wheeler Transform" in signal processing is a transformation which is used in for instance data compression and pattern recognition. It can be described in mathematical terms as: Start ...
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0answers
17 views

Generating stastical model from taxi dataset

From the dataset available here of NYC taxi journeys I wish to create some kind of model that will allow me to estimate the probability that a request comes in in a given time interval (on the order ...
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0answers
12 views

Warp shape and texture of the image into a common reference frame

I want to find object on the image using ASM and after that warp segmentation results into a common reference frame. So, I already have the algorithm of PDM and ASM and I able to find shape of object ...
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1answer
34 views

How to find equation of a curve from points

I have got a curved line that I would like to find the equation of using Microsoft Excel. The curve seems to be either a polynomial or some sort of a trig graph. I've done some research and looked at ...
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0answers
23 views

The definition of an equivalence relation in persistent homology

I am reading a paper by Carlsson on "Topological pattern recognition for point cloud data." I was having a little trouble understanding the formal definition of an ...
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1answer
15 views

Generating a deterministic random function that takes into account the date as well as a long ID

In SQL Server there's a function RAND() that if you pass a seed to it will return a pseudo random number based on the seed. No matter when you pass that same seed into this function, it will always ...
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0answers
14 views

What are the Data type for the following data set

Dear users i would like to know what are the data types of the following data set: this data set are classified the documents based on some topics , ...
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11 views

What are the appropriate statistical tests for an optimization experiment?

I recently conducted a chemistry experiment where I tried to find the optimal sugar concentration for the fastest respiration of yeast. My data looks like this: I don't have any values between 50 ...
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0answers
10 views

Using a rank sum procedure to test for differences/constructing a confidence interval for difference of medians

I was recently given a problem in which to analyze different seedling growths. I have placed my data into MiniTab combined the two groups and ranked them. This is where I am becoming a little ...
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1answer
19 views

Calculating 5 different ranges for people resource management

I am working on a project for my company. My team is building a project charter template. In this template needs to be a drop down that estimates how many full-time employee days(FTE) will be ...
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1answer
23 views

Median of Medians

Given a set A with median Am = 10 and set B with median Bm = 20 is it true that the median of the combined set C is $10 \le$ Cm$\le 20$ ? My first thought was that this wasn't true so I tried to find ...
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5answers
52 views

Prove a function is in Big-Oh and not in Big-Omega

We are told to use the definitions of Big-Oh and Big-Omega to prove that a given function is in $O(f(n))$ or $\Omega(f(n))$. It requires being able to use $c$ and $n_0$. Use the definitions to show ...
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0answers
38 views

Mixing Fuzzy Logic and Probabilistic interpretation of a dataset

A probabilistic data cloud is a set $M$ of data points $\{m_i\}_i$, where each data point $m_i$ is associated to an event $E_i$ expressing the set of the occurrences of $m_i$ in any possible ...
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1answer
49 views

Obtaining quadratic equation using Least Squares Method

This question is most likely extremely trivial, but I'm having some difficulty obtaining the least squares equation from the following data points: {{1.08, 0}, {1.07, 0.0659232}, {0.97, 0.1695168}, ...