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Sep
26
comment How to turn my data into a ROC curve in R?
So if you use one of the packages and ask the right way, it is all done for you
Sep
20
comment Numbers too large for R. How to approximate probability mass function?
+1. For an example using logs, see the code in the question math.stackexchange.com/questions/465318/… which calculates $\displaystyle\sum_{i=0}^n (-2)^i {n \choose i}\frac{(2n-i)!}{(2n)!}$ for $n= 10^6$
Sep
15
comment If I divide my data by its mean, does it still have a unit?
Unitless$\displaystyle$
Sep
15
comment Covariance of $cov(5W_7+6W_9,W_7)$ where $W_t$ is a standard Brownian motion
@Glen_b: Thank you for spotting that
Sep
14
comment Covariance of $cov(5W_7+6W_9,W_7)$ where $W_t$ is a standard Brownian motion
Your title says $cov(5W_7+6W_9,W_3)$ but your calculations use $cov(5W_7+6W_9,W_7)$.
Sep
6
comment Do mean, variance and median exist for a continuous random variable with continuous PDF over the real axis and a well defined CDF?
As for the median, you could say that the median is a closed interval, and in many examples that interval reduces to a single point.
Sep
6
comment Do mean, variance and median exist for a continuous random variable with continuous PDF over the real axis and a well defined CDF?
I would say that the second moment of a Cauchy random variable is infinite, but that its variance is not defined (since it depends on the undefined mean).
Sep
4
comment How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
@higgsss: that is the joy of the Central Limit Theorem (though this is a case of not quite independence). As I said to supercat, the likely distribution depends very much on the assumption of what are equally probable events, and that was the point I was trying to make in my initial comment.
Sep
4
comment How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
@supercat: that was the point I was making: The distribution depends on what you regard as equally probable events: there are around ${500009999 \choose 9999}$ ways of partitioning the cash total as integers but a much larger $10000^{500000000}$ ways of distributing the coins, and they lead to very different likely distributions. Incidentally, any partition of the cash total which gives unequal amounts to each person (approximately exponential or not) is as likely as any other since each can be done $10000!$ ways.
Sep
4
comment How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
Bogdan Alexandru: My algorithm (another answer) has the feature that the distribution for each individual is the same no matter whether they are chosen first, in the middle or last. It also corresponds to a uniform density across the space constrained by the total amount being allocated.
Sep
4
comment How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
Your algorithm tens to give more money to the first person than to any of the others. There are other approaches which do not have this bias.
Sep
4
comment How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
vonjd: Start with 500 million coins. Allocate each coin independently and randomly between 10 thousand individuals with equal probability. Add up how many coins each individual gets.
Sep
3
comment How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
If you give the money out one by one, there are many ways to distribute them evenly and many more to distribute them almost evenly (e.g. a distribution which is almost normal and with a mean of $50000$ and a standard deviation close to $224$)
Sep
1
comment When is beta distribution bell-shaped or concave?
@gung The black line is not concave (nor is a Gaussian density) though it might be seen as bell-shaped
Aug
3
comment Name for the Bayesian posterior probability that a regression coefficient is larger than zero
@Cam.Davidson.Pilon: I think the posterior probability the coefficient is greater than 0 is... is a better choice than anything to do with p-values
Jul
25
comment Creating a cluster analysis on multiple variables
Then you do not want to use a Euclidean metric on unscaled variables
Jul
8
comment How to treat x=0, y=0 in a linear model with no intercept?
@tiantianchen: If you assume there is no intercept then the $(0,0)$ values should give you no information about estimating $\beta$ or the uncertainty in any estimate of $\beta$ since your estimate of $\beta$ is presumably $\dfrac{\sum x_i y_i}{\sum x_i^2}$. The $(0,0)$ values do not fit your $y_i=\beta x_i + \epsilon_i$ model since they all have $\epsilon_i=0$, and so they be ignored in calculating the uncertainty in $\beta$.
Jul
7
comment How to treat x=0, y=0 in a linear model with no intercept?
As soon as you said "establish a linear relationship without intercept" you implicitly said something like "observation of values of $(0,0)$ support the assumption of no intercept, but will take no further part in estimation of the model".
Jul
3
comment History: the role of statistics in astronomy
Laplace used inverse (i.e. Bayesian) probability to give margins of error on the mass of Saturn. The Le Verrier/Adams projections which led to the discovery of Neptune were effective a form of regression.
Jul
2
comment Example of how the log-sum-exp trick works in Naive Bayes
The problem is more likely to be underflow than overflow.