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I have a data set that includes the number of visits to a website. Here are some descriptive statistics for my data
Median: 4
Mean: 14.1352
SD: 121.8119
Clearly, there are some huge values (individuals who have visited the site thousands of times.) To remove these outliers I considered simply removing any data that f... |
While it is easier to use the Pearson chi-square/Cressie-Read type test, I would like to test the equality of proportions in $k$ categories across two groups using a Kolmogorov-Smirnov type test of the form proposed by Pettitt & Stephens (1977) (see also here).
In particular as the authors of that paper point out, i... |
Let's say we have two factors (A and B), each with two levels (A1, A2 and B1, B2) and a response variable (y).
The when performing a two way ANOVA of the type:
y~A+B+A*B
We are testing three null hypothesis:
There is no difference in the means
of factor A
There is no difference
in means of factor B
There is no in... |
I know that $r$ is itself a measure of the effect size, but I would like to know if using Spearman's rank test I can argue that the relation between X and Y is significant with $r = 0.33$ and that the effect is medium, as I do with Pearson test.
|
I'm reading "The Elements of Statistical Learning" and early on there are references to p-vectors (page 10) and K-vectors (page 12).
What exactly is meant by a p-vector and K-vector?
|
Is there a software package that supports, or could support, through operator overloading or extensions, code such as the following;
x = rand_arr(10) ; array 10 elements long
y = rand_arr(10)
z = x + y ; elemental addition (z[0]=x[0]+y[0];z[1]=x[1]+y[1],...)
print z
If the above, or something similar, is valid in this... |
So I have data like:
Cost 20 30 10 5
Rating 5 3 2 5
I want to make a chart of rating vs. cost, so the points would be
[(5,20), (3,30), (2,10), (5,5)]
I can't seem to get excel to do anything other than put the two rows as independent series. Am I missing something, or I do have to pivot the data someh... |
I am fitting a conditional logistic regression model with 1:4 controls using R. I wish to obtain AIC from the model. How can I extract the appropriate parameters based on the object m?
library(survival)
m<-clogit(cc~exp+ factor1+ factor2 + strata(stratum),data=data1)
|
I am currently working on some time series data, I know I can use
LOESS/ARIMA model.
The data is written to a vector whose length is 1000, which is a queue,
updating every 15 minutes,
Thus the old data will pop out while the new data push in the vector.
I can rerun the whole model on a scheduler, e.g. retrain the m... |
I'm trying to help a scientist design a study for the occurrence of salmonella microbes. He would like to compare an experimental antimicrobial formulation against a chlorine (bleach) at poultry farms. Because background rates of salmonella differ over time, he plans to measure % poultry w/salmonella before treatment... |
Wondering if anyone has run across a package/function in R that will combine levels of a factor whose proportion of all the levels in a factor is less than some threshold? Specifically, one of the first steps in data preparation I conduct is to collapse sparse levels of factors together (say into a level called 'Other'... |
I'm a complete newbie to statistics (although I find it really interesting!), and I have taken the task of distributing feedback to speakers of a conference I'm co-organizing. Each speaker was given a grade on the scale 1-5 from the participants, and we combine feedback from all participants into a mean score, for inst... |
When computing a confidence interval of slope in linear regression, should you use the z- or t-statistic?
|
I have analyzed an experiment with a repeated measures ANOVA. The ANOVA is a 3x2x2x2x3 with 2 between-subject factors and 3 within (N = 189). Error rate is the dependent variable. The distribution of error rates has a skew of 3.64 and a kurtosis of 15.75. The skew and kurtosis are the result of 90% of the error rate me... |
Measurement outcome is a continuous number measured in $p$ locations.
This yields a vector $X_1$ to $X_p$ per subject. These vectors are obtained on $N$ subjects.
In addition these $N$ subjects come from $k$ groups.
What method should I use to compare the average vector across the entire study population to an hypothes... |
I was wondering if anyone had experience with SAS/IML and R, and can give some pointers as to the relative advantages/disadvantages of the two. I've used R extensively for programming and statistical analyses, but haven't had much experience with IML. However, as this company is a SAS shop, I'm likely to have to use it... |
I would like to know why some languages like R has both NA and NaN. What are the differences or are they equally the same? Is it really needed to have NA?
|
I'm looking into median survival using Kaplan-Meier in different states for a type of cancer. There are quite big differences between the states. How can i compare the median survival between all the states and determine which ones are significantly different from the mean median survival all across the country?
|
I wish to create a confidence interval for a statistic calculated on a table (let's say the p.value of chisqr.test).
For this, I might sample a bootstrap sample with the same size, from a table with the proportions of the table I have. And my questions are:
Is this a correct procedure to use, or is there some catch h... |
I have multiple independent coders who are trying to identify events in a time series -- in this case, watching video of face-to-face conversation and looking for particular nonverbal behaviors (e.g., head nods) and coding the time and category of each event. This data could reasonable be treated as a discrete-time se... |
Please forgive me if this is not the right Stack Exchange (and for inventing terms).
For discrete random variables X and Y, the mutual information of X and Y can be defined as follows:
$I(X;Y) = \sum_{y \in Y} \sum_{x \in X}
p(x,y) \log{ \left( \frac{p(x,y)}{p_1(x)\,p_2(y)}
... |
Greetings,
I'm performing research that will help determine the size of observed space and the time elapsed since the big bang. Hopefully you can help!
I have data conforming to a piecewise linear function on which I want to perform two linear regressions. There is a point at which the slope and intercept change, and I... |
Given $n$-vectors $x, y_1, y_2$ such that the Spearman correlation coefficient of $x$ and $y_i$ is $\rho_i = \rho(x,y_i)$, are there known bounds on the Spearman coefficient of $x$ with $y_1 + y_2$, in terms of the $\rho_i$ (and $n$, presumably)? That is, can one find (non-trivial) functions $l(\rho_1,\rho_2,n), u(\rho... |
Suppose I have a fleet of two-car trains riding around, and that each car is equipped with a data recording device. Unfortunately, some of the recording devices aren't working. I don't know either the exact size of the fleet or the percentage of failed recording devices. I'd like to make a reasonable guess about how ma... |
Occasionally I see in literature that a categorical variable such as sex is “partialled” or “regressed” out in (fixed-effects or mixed-effects) regression analysis. I'm troubled with the following practical issues involved in such a statement:
(1) Usually the coding method is not mentioned in the paper. Such a variabl... |
I'm new here and wondering if anyone could give me some hints on how to estimate the time varying coefficient and state variable together. Here is my model:
observation equation: $Y(t)= A(t)X(t)+ w(t)$,
state equation: $X(t)=\phi X(t-1)+v(t)$,
here I have time varying coefficient $A(t)$, it doesn't depend on any prede... |
I have a question on calculating James-Stein Shrinkage factor in the 1977 Scientific American paper by Bradley Efron and Carl Morris, "Stein's Paradox in Statistics".
I gathered the data for the baseball players and it is given below:
Name, avg45, avgSeason
Clemente, 0.400, 0.346
Robinson, 0.378, 0.298
Ho... |
I am running a model for a problem in insurance domain. The final results show some false positive x and some false negative y. I am using SAS Enterprise Miner for this. Can somebody suggest me how to reduce false positive? I know for this i have to increase the false negative. I want to know two things:
Is there an... |
Why the test function in Kolmogorov-Smirnov test takes the supremum of the set of differences, not maximum? When maximum (greatest element) of a set does not exist then supremum may exist, but if greatest element exist then supremum is same as greatest element. I want to know why here greatest element does not exist?
T... |
I'm working on a Monte Carlo function for valuing several assets with partially correlated returns. Currently, I just generate a covariance matrix and feed to the the rmvnorm() function in R. (Generates correlated random values.)
However, looking at the distributions of returns of an asset, it is not normally distrib... |
I try to implement a time series data analysis project, but I have to do in Java, C# or Python, is there any good libary such like LOESS, ARIMA in R you can recommend?
|
Background
I have a data set $Y$:
set.seed(0)
predictor <- c(rep(5,10), rep(10,10), rep(15,10), rep(20,10)) + rnorm(40)
response <- c(rnorm(10,1), rnorm(10,4), rnorm(10,2), rnorm(10,1))
plot(predictor, response)
and a set of models g$_i$:
fits <- list()
fits[['null']] <- lm(response ~ 1)
fits[['linear']] <- l... |
The Secretary problem
has an algorithm for fixed N and immediate accept/reject
(that is, reject reject ... accept one, stop).
There are several variants;
in mine, secretaries or samples come from a real-valued source Xj,
payoff is from best-so-far not last,
and each sample costs $ c:
maximize payoff = Xbestsofar - c * ... |
I know empirically that is the case. I have just developed models that run into this conundrum. I also suspect it is not necessarily a yes/no answer. I mean by that if both A and B are correlated with C, this may have some implication regarding the correlation between A and B. But, this implication may be weak. It ... |
If you want to regress y on x, where multiple y's are observed at each x, is it ever better to instead take the mean at each x, and the use those means for the regression? Does it depend on the distributional assumptions?
|
I have several hundred measurements. Now, I am considering utilizing some kind of software to correlate every measure with every measure. This means that there are thousands of correlations. Among these there should (statistically) be a high correlation, even if the data is completely random (each measure has only abou... |
In a double-blind study, when are deviations from the control group considered statistically significant? And is this related to the number of samples?
I realise that every experiment is different and statistical significance should depend on the deviations in measurements and the size of the sample group, but I'm hopi... |
My project is about whether early language scores (on a reading task) can predict later scores on a social attribution task. I have to conduct a logistic regression for my project but I am stuck on which one is appropriate. This is because I have conducted a binary logistic and multinomial logistic regression but I alw... |
Given a list of numbers, is it possible to find out (or in other words, is there a statistical measure to tells the) the closeness of the numbers
(do note that i am not talking about correlation - this would be for 2 sequences - something like correlation between height and weight).
I am looking for something like a cl... |
I have been confused with the problem for a very long time, and hope that somebody here can help me out.
I have a experiment installed in split-plot design, with 3 temporal groups as blocks, and 2 factors (each have 3 fixed levels) combinations in each of the block, and I have 4 replicates in each treatments. I used to... |
Suppose I am doing some experimental procedure on two treatment groups. The procedure has several stages, each of which may fail. Failure at any stage halts the experiment. If all stages are passed then there is some useful result.
Although I'm primarily interested in the final result, the treatments might also entail ... |
I have a dataset that has both continuous and categorical data. I am analyzing by using PCA and am wondering if it is fine to include the categorical variables as a part of the analysis. My understanding is that PCA can only be applied to continuous variables. Is that correct? If it cannot be used for categorical data,... |
There are 8 people playing poker.
So, the odds of winning the entire round = 1/8
2 rounds are played, and Bill wins both rounds.
What are the odds this was random? (Hypothesis test?)
NullH = Bill has no added skill. (Got lucky)
AltH = Bill has skill.
p = .13 = 1/8
q = .87 = 7/8
n = 2
SD = sqrt(pq/n) = .23
actual (p-... |
Lets say we have random variable $X$ with known variance and mean. The question is: what is the variance of $f(X)$ for some given function f. The only general method that I'm aware of is the delta method, but it gives only aproximation. Now I'm interested in $f(x)=\sqrt{x}$, but it'd be also nice to know some general m... |
Recently I have used Platt's scaling of SVM-outputs to estimate probabilities of default-events. More direct alternatives seem to be "Kernel logistic Regression" (KLR) and the related "Import Vector Machine".
Can anyone tell which kernel method giving probability-outputs is currently state of the art? Does an R-impleme... |
I am attempting to examine the change in slope between a predictor and response over two years. In year 1, it is definitely positive. (Linear regression, the 95% CI of the slope doesn't overlap 0). In year 2, the point estimate of the slope is close to 0 (0.002) and the CI overlaps 0. This is what I would expect if ... |
Background
I have a model with 17 parameters, and I currently use the coefficient of variation ($\text{CV}=\sigma/\mu$) to summarize the prior and posterior distributions of each parameter.
All of the parameters are > 0. I would also like to summarize these pdfs on a normalized scale (in this case standard deviation n... |
How can I extract the R-square from a fit rpart model?
rsq.rpart(fit)
plots the two graphs, but I simply want to extract the R-square value for the full tree.
I assume this is fairly obvious, but numerous searches didn't really lend anything useful. Any help you can provide will be greatly appreciated.
|
Given $K$ possible 'treatments' of some kind, and independent observations of some response under those treatments, say $X_{i,k}$ for $i=1,\ldots,n_k$ and $k=1,\ldots,K$, I am faced with the classical data-mining dilemma. The task is to simultaneously:
Find the treatment, say $k^*$, which maximizes effect, and
Estimat... |
Sorry if this is a n00b question, I'm just trying to wrap my head around the problem. I am trying to refute conventional wisdom here, so any help is greatly appreciated.
And now for the question:
For example, I flip a coin 100 times and I end up with 50 consecutive heads followed by 50 consecutive tails. How would I ca... |
Colleagues of mine recently presented a work where they calibrate boosted regression trees (BRT) models on small data sets ($n= 30$). They validated the models using leave-one-out cross validation (LOOCV) using R2, RMSPE and RPD indices. They also provided these indices computed by training and validating the model on ... |
One of the ANCOVA assumptions, as I read it here, says that:
Independent variables orthogonal to covariates. In traditional ANCOVA, the independents area assumed to be orthogonal to the factors. If the covariate is influenced by the categorical independents, then the control adjustment ANCOVA makes on the dependent var... |
I am a beginner level programmer preparing for the interview in medical research company. Job sounds damn interesting and I would like to get there.
To show my skills and interest, I want to write a program related to the topic.
I think, statistical analysis is quite used in that field, isn't it?
What would you suggest... |
Traffic light synchronization nowadays is not a tedious project, Image:
For a personal research project I'm trying to build a statistical model to solve such problems in two and higher dimensions.
I would like to synchronize x 4 legged (approaches) intersections such that:
The intersections are all located within th... |
I want to know if a covariate for each subject interacts with three types of trials, and the difficulty of those trials. My dependent measures are accuracy and response times (RT). For this question, I’d like to focus on RTs. Traditionally, people in my field have dichotomized the covariate of interest and used ANOVAs ... |
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 should not happen. Am I mistaken? If so why?
|
I was wondering if anybody had experience in how to set the knot points when using cubic regression splines.
Some background: I have a response and predictor variable, and I want to determine the trend relationship between the two. To see what it looks like without making too many assumptions, I've fit a smoothing spli... |
We work on cervical cancer detection and we started accumulating data in 2006 by performing HPV testing on all our samples. We have accumulated a data set with almost 400,000 women. Data enters the database on a daily basis. Most women come for a yearly smear so most women are more than one time in the database (2-13x)... |
I think it is fair to say statistics is an applied science so when averages and standard deviations are calculated it is because someone is looking to make some decisions based on those numbers.
Part of being a good statistician then I would hope is being able to "sense" when the sample data can be trusted and when so... |
In a Markov chain, a state $j$ is transient if $f_{jj}<1$ ($f_{jj}$ is probability of ever visiting state $j$ starting from state $j$ ).
Suppose, I have an irreducible transient DTMC (means all states are transient). Now, I want to prove that for any $i,j$ in $S$ ($S$ is DTMC state space), $f_{ij}$ (i.e probability of ... |
This is more of a "how to use R" question than an actual hardcore statistics question, but I think the concentration of R masters here makes this a good forum for it. I'm refreshing a time series graphing package that currently uses gnuplot. The first step is getting somewhere close to the current graphs, and then I ho... |
I have a load of point data in 3D, and I wish to cluster them like so:
Each cluster contains points all of which are at most distance $d$ from another point in the cluster.
All points in two distinct clusters are at least distance $d$ from each other.
The distances used are Euclidean distances.
Is this a well known ... |
Working on probabilistic outputs of kernel methods I found the formulation of the SVM as a Penalized Method using the Binomial Deviance (described for example in "The Elements of Statistical Learning Theory, 2nd edition" by Hastie et al., pp 426--430). The model is called "Kernel Logistic Regression (KLR)". References ... |
Can the group recommend a good introduction text/resource to applied resampling techniques? Specifically, I am interested in alternatives to classical parametric tests (e.g. t tests, ANOVA, ANCOVA) for comparing groups when assumptions such as normality are clearly violated.
An example problem type I would like to edu... |
So, working in web analytics, it's common to use a chi-square test for A/B tests to test statistical significance. I often use a calculator like this: http://www.usereffect.com/split-test-calculator , so if each variation gets 1000 impressions, and A has 100 conversions and B has 200 conversions, I know that, with a 99... |
Given a random variable $X_1$ drawn from a distribution with cdf $F$, and random variables $X_2, \cdots,X_n$ drawn from another distribution with cdf $G$, what is the formula for the probability that $X_1$ is the $k$-th out of the $n$ variables, when they are sorted in order. If it helps, assume that $F$ and $G$ are b... |
(This relates to my programming question on Stack Overflow: Bell Curve Gaussian Algorithm (Python and/or C#).)
On Answers.com, I found this simple example:
Find the arithmetic mean (average)
=> Sum of all values in the set, divided by the numbers of elements in the set
Find the sum of the squares of all values in the... |
I am working on creating a website, which displays the census data for a user selected Polygons & would like to graphically show the distribution of various parameters (one graph per parameter).
The data usually has the following properties:
The sample size tend to be large (say around 10,000 data points)
The range in... |
I am confused about how to decide whether to treat time as continuous or discrete in survival analysis. Specifically, I want to use survival analysis to identify child- and household-level variables that have the largest discrepancy in their impact on boys' versus girls' survival (up to age 5). I have a dataset of chil... |
With real-valued $X_1, X_2, \ldots$, define
$Max_n := \max(X_1,\ldots,X_n)$ record value or high-water mark
$NextMax_n :=$ the next greater high water, $Max_{n+m} > Max_n$
$Up_n := NextMax_n - Max_n$.
Can anyone suggest an introduction to estimating $NextMax$ and $Up$, for
$X$ i.i.d. from a known distribution,
nonpa... |
Lets say we have three independent variables:
$$\eqalign{
X_{1}\sim &B(n,\frac{1}{2}+\beta) \cr
X_{2}\sim &B(n,\frac{1}{2}) \cr
X_{3}\sim &B(n,\frac{1}{2}-\beta).
}$$
I'm looking for the distribution of
$$\max(X_{1},X_{2},X_{3})-\min(X_{1},X_{2},X_{3}).$$
For sufficiently large $n$ we have
$$\Pr(\max(X_{1},X_{2}... |
I would like to test a hypothesis that a database contains data that are correct in 95% or more of the samples.
I found this Hypothesis test for a proportion experiment design that looked appropriate.
I will randomly sample one-tenth of the population and mark each datum as correct or incorrect.
Here is a summary of th... |
The greatest gain of the statistics classes in both school and university seems to be that I now have an inkling of which QA site to use for this question. :)
I'm a programmer and I'm making a questionnaire with a financial background. There will be many (probably over 100) questions, which will be presented to the use... |
The probability of that a number between 1 to x is prime is $\frac{1}{\ln{x}}$ as per prime number theorem and also the total number of prime numbers between $1$ to $x$ will be $\frac{x}{\ln{x}}$.
But if we select $n$ (32 bit) random numbers, what is the probability that $p$ of them are primes?
Or Simply put
What is t... |
Any suggestions for a good source to learn MCMC methods?
|
We have a set biological samples that was pretty expensive to obtain. We put these samples through a series of tests to generate data that are used for building a predictive model. For this purpose we have divided the samples to training (70%) and testing (30%) sets. We have successfully created a model and applied it ... |
A name: first, possibly a middle, and surname.
I'm curious about how much information you can mine out of a name, using publicly available datasets. I know that you can get the following with anywhere between a low-high probability (depending on the input) using US census data:
1) Gender.
2) Race.
Facebook for instance... |
I am new to statistics so I apologize for the simplicity of my question.
I have a bag with 27 numbers inside; I will pull one number out until I get number 17. THe numbers will be returned to the bag after every try so the prob of success will always be 1/27.
I am trying to determine on average how many pulls I will n... |
Imagine a committee of people in charge of hiring a CEO. A committee member can vote "No hire" (+0), "Maybe"(+1), "Hire"(+2) for a potential CEO candidate. Each CEO is scored based on the votes, and the CEO with the highest score is hired.
Now, imagine a situation where two candidates are tied... both of them have a ... |
Given two arrays x and y, both of length n, I fit a model y = a + b*x and want to calculate a 95% confidence interval for the slope. This is (b - delta, b + delta) where b is found in the usual way and
delta = qt(0.975,df=n-2)*se.slope
and se.slope is the standard error in the slope. One way to get the standard error ... |
A recent question about alternatives to logistic regression in R yielded a variety of answers including randomForest, gbm, rpart, bayesglm, and generalized additive models. What are the practical and interpretation differences between these methods and logistic regression? What assumptions do they make (or not make) ... |
I’m writing some code (JavaScript) to compare benchmark results. I’m using the Welch T-test because the variance and/or sample size between benchmarks is most likely different. The critical value is pulled from a T-distribution table at 95% confidence (two-sided).
The Welch formula is pretty straight-forward, but I am ... |
Note: Case is n>>p
I am reading Elements of Statistical Learning and there are various mentions about the "right" way to do cross validation( e.g. page 60, page 245). Specifically, my question is how to evaluate the final model (without a separate test set) using k-fold CV or bootstrapping when there has been a model s... |
A colleague in applied statistics sent me this:
"I was wondering if you know any way
to find out the true dimension of the
domain of a function. For example, a
circle is a one dimensional function
in a two dimensional space. If I do
not know how to draw, is there a
statistic that I can compute that
t... |
The dependent variables in a MANOVA should not be "too strongly correlated". But how strong a correlation is too strong? It would be interesting to get people's opinions on this issue. For instance, would you proceed with MANOVA in the following situations?
Y1 and Y2 are correlated with $r=0.3$ and $p<0.005$
Y1 and Y... |
Are there meaningful ways to quantify how "flat" the log likelihood function is around the MLE when the parameter has more than one dimension? In particular is the determinant of the Hessian a reasonable measure?
|
Over the holidays I played a dice game where each player had 3 to 7 d6 to roll each turn. The game gave certain advantages to doubles and triples. I wanted to know the odds of rolling doubles or triples given N dice to understand the importance of "upgrading" to more dice.
My question is really about how to reason ab... |
I am analyzing an experimental data set. The data consists of a paired vector of treatment type and a binomial outcome:
Treatment Outcome
A 1
B 0
C 0
D 1
A 0
...
In the outcome column, 1 denotes a success and 0 denotes a failure. I'd like to figure out if the t... |
When teaching an introductory level class, the teachers I know tend to invent some numbers and a story in order to exemplify the method they are teaching.
What I would prefer is to tell a real story with real numbers. However, these stories needs to relate to a very tiny dataset, which enables manual calculations.
An... |
SVMs for classification make intuitive sense to me: I understand how minimizing $||\theta||^2$ yields the maximum margin. However, I don't understand that objective in the context of regression. Various texts (here and here) describe this as maximizing "flatness." Why would we want to do that? What in regression is the... |
Is there a way of plotting the regression line of a piecewise model like this, other than using lines to plot each segment separately, or using geom_smooth(aes(group=Ind), method="lm", fill=FALSE) ?
m.sqft <- mean(sqft)
model <- lm(price~sqft+I((sqft-m.sqft)*Ind))
# sqft, price: continuous variables, Ind: if sqft>mean(... |
How can a regression model be any use if you don't know the function you are trying to get the parameters for?
I saw a piece of research that said that mothers who breast fed their children were less likely to suffer diabetes in later life. The research was from a survey of some 1000 mothers and controlled for miscella... |
I understand that once we plot the values as a chart, we can identify a bimodal distribution by observing the twin-peaks, but how does one find it programmatically? (I am looking for an algorithm.)
|
I have 12 positive training sets (cancer cells treated with drugs with each of 12 different mechanisms of action). For each of these positive training sets, I would like to train a support-vector machine to distinguish it from a negative set of equal size sampled from the experiment. Each set has between 1000 and 600... |
We are working on a multivariate linear regression model. Our objective is to forecast the quarterly % growth in mortgage loans outstanding.
The independent variables are:
1) Dow Jones level.
2) % change in Dow Jones over past quarter.
3) Case Shiller housing price index.
4) % change in Case Shiller housing price in... |
I do quasi-experimental individual differences psychology research. I examine how people who differ in a cognitive ability (that I measure) perform on another task that always at least involves within-subject manipulations (and sometimes between-subject)–DVs are usually response time and/or accuracy. For this question ... |
I'm doing some software testing where we are measuring specific latencies. Generally we run the same test several times to just eyeball the results and make sure that they are consistent across runs. I usually do this by plotting the cumulative distributions for each run together on a graph, and look for an anomalies... |
Let's say we have two biased coins. The probability of tossing a head on the first coin is $\alpha$ and the probability of tossing a head on the second coin is $1-\alpha$. We toss both coins $n$ times and we say that there is a success when there is a head on both coins. If we denote this random variable by $X$ then
$$... |
This probably seems like a really strange question, but let me try to explain what I want to do; hopefully it will make sense.
I have a data set with a couple dozen variables, such as age, level of education, self-assessed (via a Likert scale) measures of technical ability, experience, willingness to share personal inf... |
We are trying to make simulation experiment involving a common stochastic trend, that is described by the random walk (or $I(1)$ process) $Y_t = Y_{t-1} + \varepsilon_t$, where innovations $\varepsilon_t$ ~ $N(0,1)$. However when could we be sure that the past innovations are more or less reasonably included into the s... |
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