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# Actuarial Mathematics - Science topic

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Hi frds,
What calculation formula and hypotheses do actuaries currently use for the assessment of the impact of Covid and Long Covid on life expectancy in years?
How long does it historically take to integrate new diseases in formulas? 2 years? 5 years? 15 years?
Dear Thomas Schuermann,
Different risk categories grew during each wave of the SARS-CoV-2 (Covid-19) coronavirus pandemic. On the other hand, each successive wave of the pandemic generated smaller and smaller escalation scales of many risk categories. In particular, the development of highly effective vaccines against the coronavirus and the introduction of nationwide universal vaccination programs for citizens against Covid-19 has reduced the scales of potential different risk categories.
Kind regards,
Dariusz Prokopowicz
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I am working on portfolio optimization using lower partial moment of order 1, can someone help me how to implement LPM-1 in excel sheet using "tau" as my threshold value as 0.00% and order (n) as 1.
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How to find the distance from C to S in this 3D Ellipsoid .And the how to get the distance D between two foci ? Let say coordiantes a=5, b=4, c=4.
Question 3. The Distance between -C to S and between S to C must be equal to 2a. Can anyone solve it with example please?
I assume that a,b,c are the lengths of semi-axis. The distance CS=a=5.
In the first example where b=c is this elipsoid a solid of revolution, thus the foci of the ellipse are also foci of the solid.
Given a=5, b=4 we can compute the focal distance with the use of Pythagorean theorem: (D/2)2=52-42=9. Thus D/2=3 and D=6.
If a=5, b=4, c=3 is the solid different, but the situation in the plane (F1F2S) is as above. D=6.
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I have a function as follows:
y= a*x^b
a=7e-5
b=-0.755
I attached a simple graph of the function. As it is apparent from the graph the CURVATURE of the function increases from ZERO to a finite value (around x=0.1-0.2) and then it decreases to reach a value of ZERO. I did my best to draw the CURVATURE of this function using the following formula:
K=f"/(1+f'^2)^1.5
However, using this formula I could not reach the predictable trend of the curvature. Do you have any idea what is the problem?
I can work with MATLAB and Excel.
Kind regards,
Ebrahim
Check the power index in the denominator of your expression for the curvature. It should be 3/2 rather than 1/2. Good luck
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Project management in research project
Yes, it is one of the foundations of research
Best Regards Javan Gh. Doloei
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Do you think that the iThenticate/CrossCheck/Similarity Index would cause heavy and serious confusion in mathematics? Even destroy, ruin, damage Mathematics? Our mathematics and mathematicians should follow and inherite symbols, phrases, terminology, notions, notations in previous papers, but now we have to change these to avoid, to escape, to hide, to decrease the iThenticate/CrossCheck/Similarity Index! It’s very ridiculous for mathematics and mathematicians! Mathematics is disappearing! being damaged!
Yes! Even standard mathematical symbols and notations are captured in similarity index. The habit of using unconventional symbols and notations just to reduce similarity index is destroying the beauty and taste of mathematics.
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After estimating an ARDL model in eviews, you can ask for the long run coefficients by clicking view > coefficients diagnostic > long run form and bound test. My question is: how standard errors of the long run coefficients are calculated? I know they are related to "Delta method" and I tried to search more about it and how standard errors of the long run coefficients are calculated in eviews user guide, but I couldn't.
I would appreciate any guide in how to calculate standard errors of the long coefficients.
Thanks & regards.
see for instance on the internet the stata explanation: http://www.stata.com/support/faqs/statistics/delta-method
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Some of students ask me to give the applications of mathematics in real life. What are some of the interesting applications of mathematics in real life? Could you please share your knowledge about this issue.
You are asking about millions of mathematical application in our life, like calculation of area, volume, velocity, acceleration ....etc.
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In linear stability analysis of double diffusive convection can anyone  please tell that how perturbation equations (1) in the link is achieved. I am confused.
Hi Faria,
I am assuming that you are happy with what the full perturbation equationss are, from which those equations (1) have been derived. I am also assuming that you need to know why (1) is correct for tall salt fingers.
The derivation follows directly from the assumption that z is very large compared with x and y for the salt fingers. Mathematically, if z >> x, then d/dz << d/dx. Physically this corresponds to saying that the distance over which variations take place in the x-direction is much smaller than the distance in the z-direction, and therefore x-derivatives are much large than z-derivatives. If one imagines a single convection cell in a very tall cavity, then hopefully (!) it will be clear.
Therefore w_xx+w_yy+w_zz is well-approximated by w_xx+w_yy because w_zz is negligible.
Essentially this is an order-of-magnitude analysis of the type that one uses in boundary layer theory.
Cheers,
Andrew
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Hi RGaters,
Does anyone know how to modify the order in a sample to modify Kendall's tau value(s) ? Let me clarify what I am looking for. Consider that we have N realizations of K random variables. Each realizations of the group of K variables is independent from the other ones. Inside this realization, the K variables might be independent or not, we do not really care. They even can follow different distributions. The question is the following : from any sample (size N x K) that we call M, can I exchange the places of M[i_1,1] with M[i_2,1], M[i_3,2] with M[i_4,2] and so on, possibly coming back to the first column with an interative algorithm to finally obtain as a result a new (rearranged) sample M' where tau[1,2] = first wanted value, tau[1,3] = second wanted value, and so on, i.e. can I get rearranged data to get a desired tau-matrix. If yes, any algorithm to suggest ?
I used Cholesky method to do the same thing to reach a desired Pearson-correlation matrix, but I have to admit I'm facing a wall on this issue right now.
Any help is welcome !
Hi René,
Thanks for your answer, however, I work in practice with 100 000 * 10 (it's true that I did not mentioned this above) matrices that I want to rearrange this sample to reach a target kendall's tau matrix (as close as possible). It is not the kendall's tau matrix that I want to rearrange, it is the data which lead to this kendall's tau matrix. That'd be too easy :)
Considering this, there is absolutely no way that I try every possible combinations and see which one to choose. I need some intelligent trick such as Cholesky method to get correlate variables.
So basically, it's not only about programming skills, it's also about applied mathematics.
Best regards !
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What are the latest research on bath tub shaped failure rate functions?
Sure,
its a standard survival analysis text, most of the focus is on standard non/semi parametric approaches (ie Kaplan-Meier / Cox models), but early on there is a good discussion around parametric models and model fitting as I recall.
Survival Analysis: Techniques for Censored and Truncated Data (Statistics for Biology and Health) Hardcover – March 10, 2005
by John P. Klein (Author), Melvin L. Moeschberger (Author)
ISBN-13: 978-0387953991 ISBN-10: 038795399X Edition: 2nd
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It is well know that each Borel measure m on metric space is regular, i.e. for Borel set A and any d>0 there are open set G and close set F, such that F\subset A\subset G and m(G\F)<d. Is there constructive proof of this fact in the sense that using set A we can build up the sets F and G? Is there procedure of building F and G?
This is a good question.
Regularity is important in the description of multiscale measures and functions.  This is central theme in
M.L Lapidus, J.A. Rock, Toward zeta functions and complex dimensions of multifractals, arXiv 0810, 2008, no. 0789v1,  1-16,  downloadable from RG.
The regularity of a Borel measure is defined on page 3 (see Def. 2.1).   Partition zeta functions are introduced in Section 4, starting on page 8, defined for any Borel measure.   See Theorem 5.2, starting on page 12, the regularity of a Borel measure is considered.
Reverse mathematics is considered in proving the measure-theoretic regularity in the Borel hierarchy in
S.G. Simpson, Mass problems and measure-theoretic regularity, Penn. State University, 2014:
See Section 7, starting on page 20.   There are lots of interesting results in this section.
It is proved that the outer regularity of locally finite Borel measures in metric spaces in
J.T. Tyson, Metric and geometric quasiconformality in Ahlfors regular Loewner spaces,  Conformal Geometry and Dynamics 5, 2001, 21-73:
See Proposition 1.4, starting on page 27.
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At the moment I am trying to judge the validity of a model assuming a CARA-Utility-Function. And I vaguely remember that experimental results usually suggest decreasing absolute risk aversion.
Unfortunately I cannot find any literature on estimations of risk-aversion and its behavior when stakes get higher at all.
Are there papers like this?
Michael
Looking at some of the early works Pratt and Arrow may help.
Check out these papers:
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Let me correct your question to the following one: how could I apprioximate a nonlinear term by a linear one? Detailed answer must be based on formulation of your problem.
1) For instance, if your problem concerns a nonlinear partial differential equation (NPDE) of the following form (H+eV)f=r, where H is linear operator, V is your non-linear term, e is perturbation small parameter and f is your target then you can apply perturbation method.
2) There are nonlinear problems which can be solved exactly. For instance there is class 1+1 dimensional of NPDE which can be handled by Inverse scattering method, or by the Backlund transformation. Et cetera. Display more about your problem.
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