The expected value of a random variable; or a location measure for a sample.

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970 views

PCA on non-centered data [duplicate]

How does the mean influence PCA? What happens if I use PCA on data with a mean $\ne0$?
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1answer
76 views

How to convert mean and standard deviation to a single meaningful and quantifiable value?

I look at mean and standard deviation of various map like data and each give meaningful information but sometimes they provide different information. For example, let's take states in a country. One ...
2
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2answers
89 views

Bivariate Normal Distribution Mean

$X$ and $Y$ have bivariate normal distribution and have joint pdf \begin{equation*} f\left( x,y\right) =a\exp \left( \frac{-1}{2}\omega \right) ,\text{where }% \omega =6x^{2}+12y^{2}-16xy-8x+24 ...
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2answers
256 views

Expected sum of money

There is a little problem in the working on this one I have encountered recently. Here it goes: Starting off with \$100, when you toss a coin, if there is a tail, you will get \$10 and lose $10 if it ...
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1answer
84 views

How to find the probability that a random sample of 10 points out of 52 points of data will have a mean close to the total mean?

I have a data set that consists of 52 weeks of data. I want to find the probability that any 10 weeks of data within the set of 52 weeks is close to the mean of the total 52 weeks. Close meaning ...
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0answers
50 views

Standard mean and deviation

A company supplies specialized high-tensile pins to a customer.It uses an automatic lathe to produce the pins.Due to factors such as vibration, temperature and wear and tear, the lengths of pins are ...
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1answer
55 views

How to make sense of 6mo worth of weight loss data?

-I have ~6mo of data that contains daily weight/caloric intake & #carbs/fats/proteins. I'm trying to figure out a way to make sense of the data. It's not a perfect experiment so there are other ...
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1answer
135 views

What is the sample-size range for which the median should be preferred to the mean as a measure of central tendency? And why?

I have firing-rate data for neurons ranging from 40-60 in number for various experimental groups. I've seen both mean and median being used in the literature, but without much explanation for the ...
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0answers
42 views

Which is the correct mean?

My colleague and I disagree on the following data, and the calculation of the mean: Given $n$ respondents, each respondent has three chances to score a hoop at basketball. A respondent has 'hooped' ...
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2answers
950 views

Overdispersion in logistic regression

I'm trying to get a handle on the concept of overdispersion in logistic regression. I've read that overdispersion is when observed variance of a response variable is greater than would be expected ...
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1answer
103 views

$E(\overline{x})$ vs $E(x)$?

If I have a problem down to $$k(E(x^2) - E(x)^2) = E(\overline{x}^2) - E(\overline{x})^2$$ ...can I say $k = 1$? $X$ has an unbiased mean and a variance. Each $x$ in $X$ is independent. Or is it ...
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1answer
3k views

How can a distribution have infinite mean and variance?

It would be appreciated if the following examples could be given: A distribution with infinite mean and infinite variance. A distribution with infinite mean and finite variance. A distribution with ...
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1answer
146 views

Find minimum number of batteries to last a week with 95% probability given mean and sd of lifetime

A TA needs a very important program on his computer but his power cable is missing. Luckily, he happens to have 100 batteries lying around and a contraption that can store batteries to use one at a ...
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1answer
99 views

fraction of geometric means versus fraction of arithmetic means

Ideally, I would like to know the fraction of the mean of $x$ over the sum of the mean of $x$ and the mean of $y$: $$\text{Fraction of interest} = \frac{\bar{x}}{\bar{x}+\bar{y}}$$ where $$\bar{x} = ...
2
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1answer
159 views

Finding the cluster centers in kernel k-means clustering

I think this is the most easily understood topic in Kernel K Means Clustering. But assuming that I am not an expert in Machine Learning, can someone tell me how does someone calculate Kernel K means ...
5
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1answer
156 views

Was the math/statistics application in this article correct?

I don't know high level math or statistics and wanted to ask about the math in a recent online article. The website 'TheMarySue.com' has an article saying: ON AVERAGE, THE TOP WOMEN-LED FILMS OF ...
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1answer
281 views

Do the mean and the variance always exist for exponential family distributions?

Assume a scalar random variable $X$ belongs to a vector-parameter exponential family with p.d.f. $$ f_X(x|\boldsymbol \theta) = h(x) \exp\left(\sum_{i=1}^s \eta_i({\boldsymbol \theta}) T_i(x) - ...
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1answer
332 views

Confidence interval does not include 0, but Wilcoxon test is sgnificant

I've created an error plot with CI 95% to visualize the difference (post test - pre test) between achieved scores. n = 64 Judging from the confidence intervals one could conclude that there's is ...
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3answers
3k views

What are the relative merits of Winsorizing vs. Trimming data?

Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values. I always see ...
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1answer
26 views

Creating a translated sample by subtracting mode

Consider a sample $x_1,...,x_n$ which we will call the original sample. To create a translated sample $x_1+c,...,x_n+c$, we add a constant $c$ to each sample point. Let $y_i=x_i+c, ...
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2answers
64 views

Padding a matrix - effect on statistical analyses

I have the time-series data for a lot of stocks from their specific groups (market indices), and I would like to perform some quantitative tests on them as a group. Let's say for example I have 30 ...
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1answer
55 views

Is it ok to compute statistics on t-values?

Background I have a population in which my dependent variable is binary with a highly-skewed distribution: Very few records are 1 (doers), most records are 0 (non-doers). I'm using logistic ...
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1answer
289 views

Arithmetic vs Geometric Mean

There are verbal suggestions everywhere on when one should use a geometric average or when an arithmetic average should be preferred, but I can't find any formal statistical treatment of this ...
3
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1answer
78 views

Summarising simulations on a transformed parameter

Let $\theta > 0$ be some model parameter for which properties (bias, ...) of an estimate are studied via simulations. For a given data set, an estimate $\hat{\theta}_i$ of $\theta$ can be ...
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1answer
244 views

Calculating Confidence Interval

How would one go solving for this? You are told that a 95% CI for expected lead content when traffic flow is 15, based on a sample of n = 12 observations, is (468.1, 591.7). Calculate a CI with ...
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1answer
61 views

What can be inferred when multivariable ordinary least squares and quantile (median) regression yield differing results?

There lies information in a discrepancy of the (unconditional) mean and median. For example, if the median is larger than the mean, the distribution must be left-skewed. Does this kind of inference ...
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4k views

In left skewed data, what is the relationship between mean and median?

I think the median $\leq$ mean. Is this the case?
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1answer
110 views

Coverage Proof of Confidence Intervals

The confidence interval for the mean of a random variable $Y$ has coverage $1-\alpha$ which I am trying to show. Starting from $$\widehat{E(Y)} - ...
2
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1answer
89 views

Advantages of bootstrapping when calculating mean

I'm a statistically incompetent social scientist who is very much out of my depth... I'm using R to analyse a data set, which is a 1% sample of a population showing cancer rates across 20 regions. ...
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1answer
157 views

comparing means between different studies

In a questionnaire, I have asked some Likert scale questions. These questions were asked to the same population 6 years ago in another study. I only have the mean scores and standard deviation of the ...
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1answer
112 views

Is the bootstrap estimate of the mean biased when a single extreme value is in the sample?

My sample includes $n$ random observations, while $n-1$ of these observations are in the range (0-1) there is also one observation that gets very high value. For example, a sample of prices where ...
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0answers
20 views

Understanding (1-mean(L) - c*(stderr(L))

I inherited some old programming code for a scoring mechanism and I am trying to understand it. The premise is that every user $u$ has receives many ratings from other users, all in the range $[0, ...
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2answers
46 views

Can you have constant mean across samples with different distributions?

This might be a stupid question - but can data samples have constant means even if they are from different distributions?
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1answer
170 views

Taylor expansion to contain sample mean, sample variance, sample skewness, and sample kurtosis

I have the following expression: $$\frac{1}{p} \ln\left(1+\frac{p^1}{1!n}\sum_{i=1}^n x_i + \frac{p^2}{2!n} \sum_{i=1}^n x_i^2 + \frac{p^3}{3!n} \sum_{i=1}^n x_i^3 + \frac{p^4}{4!n} \sum_{i=1}^n ...
0
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1answer
46 views

Changing a multivariate Gaussian along a dimension

I have a multivariate Gaussian parameterised by a mean vector $\mu$ and a precision matrix $\Sigma$. Now, I want to set the Gaussian along a given dimension $i$ to a point mass i.e. I set the ...
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0answers
4k views

When is a sample proportion p hat instead of x bar

I just started my first statistics class and am not majoring in statistics so sorry if this sounds like a beginner question and also sorry if my language is incorrect. (feel free to correct me.) I ...
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0answers
91 views

Asymmetric confidence intervals on bootstrap estimates

I've performed bootstrapping on my leastsq parameters and now I have a load of data from which I can get the mean and standard deviation for each parameter. Lovely. But when I look at a histogram of ...
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0answers
64 views

Calculating the variance of sample mean?

I am working on time series analysis. The book I am using ("Statistics for Long Memory Processes" by Jan Beran) uses a number of measures for process memory and one of them is to graph Sample Mean ...
4
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3answers
634 views

Variance of the sum of a Poisson-distributed random number of (normally distributed) random variables

Suppose I have a fruit stand where I sell oranges. Every day I have an average of $\lambda$ people (Poisson distributed) each buying a normally distributed weight quantity of oranges with mean $\mu$ ...
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0answers
58 views

Proof for mean and variance of a multidimensional half normal distribution

Given a $p$-dimensional random variable $\xi \sim \mathcal{N}\left( 0, I_{p} \right)$ and a $p\times p$ dimensional diagonal matrix $\Lambda$ with diagonal entries $\lambda = \left( ...
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0answers
155 views

Poisson Distribution of a radioactive decay

You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a ...
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0answers
90 views

can I compute the product of these two multivariate normal densities in a simple way

I have two multivariate normal densities and I parameterise them by the precision matrix (i.e. the inverse covariance matrix). One of them has a sparse precision matrix and the other one has a simple ...
0
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1answer
196 views

test for comparing means of two time series [duplicate]

I wonder if there is a test for comparing means of two different time series (both measured at the same person or two different persons)? Would be very glad if someone can help me!
3
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0answers
548 views

Confidence interval for the restricted mean in survival analysis

What is the recommended way of calculating confidence intervals for the restricted mean in survival analysis? Here are some example data, taken from the paper Chris Barker (2009), The Mean, Median, ...
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0answers
67 views

Comparing three means

I'm performing a meta-analysis but I have a question: I'm evaluating three different treatment strategies (A,B,C) for each of those treatment strategies I have around 20 papers describing outcomes. ...
5
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1answer
94 views

When estimating population mean, how can one half of the sample mean have lower risk than the sample mean itself?

I read Efron and Morris (1977) Stein's Paradox in Statistics with interest yesterday and stumbled upon the statement that, if and only if the population mean is close to zero, than the risk (mean ...
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1answer
73 views

A question on sampling distributions

I once read the following interesting distribution related question: An insurance company identified the 10 safest and 10 least-safe cities from 200 cities in the US based on the mean number ...
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1answer
132 views

standard deviation help [duplicate]

A tire manufacturer believes that the tread-life of its snow tires can be described by a normal model with a mean of 32 thousand miles and standard deviation of 2.5 thousand miles. Based on this ...
2
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1answer
133 views

Testing whether the mean of a group is different from the mean of the entire sample

I have the mean and standard deviation of a large sample (30k obs) and the mean and std of a subsample (2k obs). The means are percentage figures (i.e. between 0 and 100% and hence not a normal ...
3
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1answer
195 views

Why are statistical properties of mode and median difficult to determine?

I have read a book saying that statistical properties of the mode and the median are difficult to determine compared to the mean. I am not entirely sure why is so. Is it correct that because the mean ...