All Questions
Tagged with ordinary-differential-equations statistics
50
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What's the explicit difference when looking at Differential Equations vs Stochastic Differential Equations?
I learned differential equations from mathematics text and have having some trouble with its application in statistics. Specifically applied to stochastic time series.
From my time series text reads "...
- 365
3
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1
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318
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Geodesics of Fisher-Rao metric on the open interior of the finite-dimensional simplex.
I am curious about the explicit form of the geodesics of the Fisher-Rao metric tensor on the open interior of the n-dimensional simplex.
In the 2-dimensional case (only 1 parameter on the 2-simplex), ...
- 1,322
-2
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2
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419
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Pareto PDF differentiation gives a negative CDF
I am trying to calculate the CDF based on the PDF for the Pareto distribution, I've done the differentiation but I end up with a negative functionlike: $-(\frac{\lambda}{(x+\lambda)})^\alpha$
The ...
- 9
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Comparing Standard Errors, t-Statistics, P-Values, Logistic Curve Fitting Exercise [duplicate]
I have two growth curve data sets, A (Martians) and B (Venusians). Data point sets of age (0 (birth) - 250 months, X axis) against height (0 - 200 centimeters, Y axis). The first set (A) contains 67 X ...
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578
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Solving equation involving error function and normal distribution
Let $\phi(x)$ be a normal distribution, that is $\phi=\frac{1}{\sigma}\phi(x|\mu,\sigma^2)$ and $\Phi(x)$ be the CDF of $\phi$, i.e., $\Phi(x|\mu,\sigma^2)=\frac{1}{2}[1+erf(\frac{x-\mu}{\sqrt{2}\...
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2
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351
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Is jump intensity inaccurate in describing random process?
In https://en.wikipedia.org/wiki/It%C3%B4's_lemma
Under the section of Poisson jump processes, it is said that
We may also define functions on discontinuous stochastic processes.
Let h be the jump ...
- 948
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0
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40
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how to model the transient response of a function in 1D
I have a fairly simple problem. Here is the statement:
I know $f(x,t)$ over a period of time. I want to model its evolution, i.e. $\frac{\partial f(x,t)}{\partial t}$. But the transient response is ...
- 387
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1
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879
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Which are the most fundamental theorems in core undergrad math? [closed]
I want to compile the most important theorems for Calculus, Linear Algebra, and introductory ODE, PDE, probability and statistics.
These should be the most important 5/10 per "subject", to put an ...
- 215
1
vote
1
answer
418
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writing a piecewise regression model as a linear model
lets write the following piecewise regression model
$$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0 $$
$$ y=\beta_0 +\beta_1 x + \epsilon \ \ x\gt x_0$$
according to the variable $x_0$ is known,...
- 6,510
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59
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Where can I find this definition of "expected value"?
I need bibliography or some text about this definition:
"Define the expected value of a function by:
$E_{t}(x(t))=(\frac{1}{t})\int_{0}^{t} x(s)ds$. "
I think that it's statistics or functional ...
- 85
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0
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158
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Stable distribution law related to the Dickman function
It is known that if $U$ is a random variable with uniform distribution on the interval $(0,1]$, then the random variable defined as
$$
X\stackrel{d}{=} U^{1/\alpha}(1+X)
$$
where $\alpha>0$ ...
- 765
1
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1
answer
2k
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Finding mean and variance of stochastic process
If I'm given a Stochastic Process Xt that satisfies a stochastic diff. equation, let's say fXt,
what is the formula to find the mean and variance of Xt?
I think it's:
$mean = dE(X_t) = dX_0e^t$
$...
- 13
1
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1
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2k
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Just learned about the bell curve in statistics. How is calculus related to this curve?
I'm learning about the bell curve in statistics and I'm trying to understand the calculus behind the concept. I've taken calc 1 already. How is the integral related to this ...
- 319
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1
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345
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How are moments used in crystallization population balance calculations?
For example in this paper http://konyvtar.uni-pannon.hu/hjic/HJIC35_07_17.pdf method of moments is used to describe crystal size and other parameters. Can somebody explain how to relate normal method ...
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318
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How to find variance of a CIR process
CIR process is defined as follows:
http://en.wikipedia.org/wiki/CIR_process
I get an SDE form for d_Vt/dt, but can't proceed further.
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