How do I get the approximation of a falling factorial?

I found an approximation in falling factorial. It says that: (a)n-1=a(a-1)(a-2)...(a-n+2) approximate to [a-(n-2)/2]n-1. Can someone tell me how to derive the approximation?

11 December 2014 1,746 4 View

Can you help me with this approximation of falling factorial?

I am working on my undergraduate thesis. I am using a paper that I attached below. When I solving a polynomial with (n-1) degree from a falling factorial, the paper use this...

11 December 2014 9,519 0 View

How do I construct a joint pdf for a uniformly distributed sample that is drawn without replacement?

I have a sample X1, X2,..., Xn that drawn from uniformly distributed population. The sample drawn without replacement. Since it depends each other (which is not i.i.d), the joint pdf is not the...

10 November 2014 2,315 4 View

How do I calculate the summation of p.d.f. from a discrete uniform distribution where the parameter space is infinite?

Summation of p.d.f. from any discrete distribution are always 1, where its fulfill the law of a probability. But when we have a discrete uniform distribution with infinite parameter space. Does...

09 October 2014 1,264 5 View

How do I prove that a statistic is appropriate to estimate a parameter?

08 September 2014 4,669 4 View

Can we easily use improper prior distribution as a prior in Bayesian estimation?

Improper distribution is the distribution which doesn't integrate to 1. For example, Improper Uniform Prior Distribution for all positive integers. This distribution integrate to infinity. Is it...

07 August 2014 2,848 1 View

Can anyone give me an interpretation or link about improper uniform prior as a prior distribution in Bayesian estimation?

I need a good reason why improper uniform prior could be use as a prior in Serial Numbered Population (SNP) problem. Or maybe someone can tell me about improper uniform prior itself. An pdf link...

07 August 2014 9,224 5 View

Could you recommend any books about Number Theory?

Beginner level books. High level books. Analytical Number Theory. Algebraic Number Theory. Combinatorical Number Theory. Books about partitions. Books about primes.

03 March 2021 7,174 5 View

Arena simulation - how do i model the following model in ARENA (see description) (new to ARENA)?

Hello, I'm fairly new to ARENA and I have the following problem: I have two queues in which, in each queue, a different order type arrives (both having an arrival rate of exponential 10). Order...

02 March 2021 2,431 3 View

Is there a deep reason for using the squared modulus of the wave function as the probability density of the existence of the particle?

I think we were all surprised at the first time we got to know quantum mechanics that the squared modulus of the wave function is the probability density of the existence of the particle? The role...

28 February 2021 6,282 9 View

What is Flat Lens Antenna?

28 February 2021 5,433 3 View

Can impedance of antenna be less than 50 ohms?

I am simulating helix antenna in hfss, right now, giving excitation with 50 ohms port. When I see the results of Z parameter (real). It shows lower than 50 ohms. Do not understand, if it can be...

27 February 2021 4,218 7 View

What are the application of Fixed points thoery in Chemistry.?

It is said that fixed point theory has lot of applications not in the field of mathematics only but also in various areas. So I am looking for applications in Chemistry only..

26 February 2021 3,533 1 View

How to compare 2 samples recruited with different sampling methods?

If I want to compare characteristics of 2 groups of patients, one group is recruited from a random sample of the general public while another group is from a sample with a fixed gender (male to...

26 February 2021 3,526 3 View

How to plot the probability paper of Gumbel distribution using R programing?

In R-studio, there are many commands of Gumbel package. Arguments are also different. I`m asking about the alpha parameter of the Copula which must be greater than 1. If this is the one used to...

25 February 2021 5,229 3 View

How to interpolate from a time-series database ?

Hi, I am having trouble with a problem, in the field of Optimal Control and the generation of optimal time-series. Let's consider a system, whose dynamics are represented by dx/dt =...

24 February 2021 9,105 2 View

Bayesian decision trees and bayesian regression trees in Python and/or R?

I am looking for implementation of bayesian decision trees and bayesian regression trees in Python and/or R.. Do you know if the existing libraries support this

23 February 2021 6,689 3 View