I have distance value between two objects. Need algorithm to check whether measured distanced is available in distance of any two objects in grid pattern shown in Image
Grid for verification
This is grid with squared cells. All distances at such grid (expressed in units of cell size) should satisfy to condition
d^2 = a^2 + b^2
If squared distance is integer and you can represent it as sum of two integer squares, then objects can be placed in grid nodes.
There is mathematical criteria - number P is not representable as sum of two squares if it's factorization into primes contains any (4n+3)factor in odd power
I want to know is there a function to calculate the inverse cdf of poisson distribution? So that I can use inverse CDF of poisson to generate a set of poisson distributed random number.
A) Inverse CDF of Poisson distribution
The inverse CDF at q is also referred to as the q quantile of a distribution. For a discrete distribution distribution . the inverse CDF at q is the smallest integer x such that CDF[dist,x]≥q.. The Poisson distribution is a discrete distribution that models the number of events based on a constant rate of occurrence. The Poisson distribution can be used as an approximation to the binomial when the number of independent trials is large and the probability of success is small. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute.
Formula
The probability mass function (PMF) is:
mean = λ
variance = λ
Notation
Term Description
e base of the natural logarithm
Reference: Methods and Formulas for Inverse Cumulative Distribution Functions
B) Excel Function: Excel provides the following function for the Poisson distribution:
POISSON(x, μ, cum)
where μ = the mean of the distribution and cum takes the values TRUE and FALSE
POISSON(x, μ, FALSE) = probability density function value f(x) at the value x for the Poisson distribution with mean μ.
POISSON(x, μ, TRUE)= cumulative probability distribution function F(x) at the value x for the Poisson distribution with mean μ.
Excel 2010/2013/2016 provide the additional function POISSON.DIST which is equivalent to POISSON.
Reference: Office Support POISSON.DIST Function
C) Excel doesn’t provide a worksheet function for the inverse of the Poisson distribution.
Instead you can use the following function provided by the Real Statistics Resource Pack. It’s a free download for Excel various versions.
POISSON_INV(p, μ) = smallest integer x such that POISSON(x, μ, TRUE) ≥ p
Note that the maximum value of x is 1,024,000,000. A value higher than this indicates an error.
Reference: Real Statistics Using Excel
D)
Reference to MREXCEL.COM web site a query related to your question quoted below seems to be related to your question.
Not sure if anyone can help with this. Basically I'm trying to find out how to apply the reverse of the Poisson function in excel. So as of now I have poisson(x value, mean, true-cumulative) and that lets me get the probability for that occurence. Basically I want to know how I can get the minimum/maximum x value based on a given probability.
So if I have a list of data (700 rows) and I want to find out what the minimum starting value should be given a desired average and the fact that I want the lowest value to be at the 0.05% probability. So 0.05% = (x, 35, True) solve for x. I know I can prob do this with solver, but I am trying to figure out a way to do this formulaicly without having to use the solver (as I may have to use this many times).
The code referred to here covers the inverse of the poisson formula when using True in the excel formula. It does not cover the inverse of the poisson formula when using False in the excel formula.
Re: Reverse Poisson?
Originally Posted by shg
A further mod to accommodate large means:
Code:
Function PoissonInv(Prob As Double, Mean As Double) As Variant
' shg 2011, 2012, 2014, 2015-0415
' For a Poisson process with mean Mean, returns a three-element array:
' o The smallest integer N such that POISSON(N, Mean, True) >= Prob
' o The CDF for N-1 (which is < Prob)
' o The CDF for N (which is >= Prob)
-------Reference :> https://www.mrexcel.com/forum/excel-questions/507508-reverse-poisson-2.html>
E) Why doesn't Excel have a POISSON.INV function?
Discussion on Referred web page have references to some formulas for calculating related information desired by OP.
You could use the following.
With the Poisson mean named lambda, enter the following in an newly inserted worksheet.
A1: =IF(ROWS(A$1:A1)<=4*lambda,POISSON(ROWS(A$1:A1)-1,lambda,1))
Fill A1 down into A2:A1000 (4 times as many rows as your most typical lambda value). Name the A1:A1000 range POISSON.CDF. Then use the formula
=MATCH(n,POISSON.CDF)-1
to give the results a POISSON.INV(n,lambda) function would.
If you want this for varying lambda, use the array formula
=MATCH(n,POISSON(ROW($A$1:INDEX($A:$A,4*lambda+1),lambda,1))-1
Reference Shared Link
Hope That Helps.
=MATCH(RAND(),MMULT((ROW(INDIRECT(ADDRESS(1,1)&":"&ADDRESS(MAX(lambda,5+lambda* 45/50)+6* SQRT(lambda)+3,1)))=COLUMN(INDIRECT(ADDRESS(1,1)&":"&ADDRESS(1,MAX(lambda,5+lambda* 45/50)+6* SQRT(lambda)+2))))+0,MMULT((ROW(INDIRECT(ADDRESS(1,1)&":"&ADDRESS(MAX(lambda,5+lambda* 45/50)+6* SQRT(lambda)+2,1)))=(COLUMN(INDIRECT(ADDRESS(1,1)&":"&ADDRESS(1,MAX(lambda,5+lambda* 45/50)+6* SQRT(lambda)+1)))+1))+0,POISSON(ROW($A$1:INDEX($A:$A,MAX(lambda,5+lambda* 45/50)+6* SQRT(lambda)+1))-1,lambda,1)))+(ROW(INDIRECT(ADDRESS(1,1)&":"&ADDRESS(MAX(lambda,5+lambda* 45/50)+6* SQRT(lambda)+3,1)))=(COLUMN(INDIRECT(ADDRESS(1,1)&":"&ADDRESS(1,1)))+FLOOR(MAX(lambda,5+lambda* 45/50)+6* SQRT(lambda)+2,1)))+0)-1
It is quite slow for lambda >1000.
This expands on the array formula
=MATCH(C4,POISSON(ROW($A$1:INDEX($A:$A,4*lambda+1)),lambda,1))-1
shared above by skkakkar, by prepending the array with 0 and appending with 1, following Is there a way to concatenate two arrays in Excel without VBA? .
The rest is mostly making the array shorter by replacing 4* lambda with 6* SQRT(lambda).
what is the actual formula to compute sentiments using sentiment rated lexicon. the lexicon that I am using contains rating between the range -5 to 5. I want to compute sentiment for individual sentences. Either i have to compute average of all sentiment ranked words in sentence or only sum up them.
There are several methods for computing an index from scored sentiment components of sentences. Each is based on comparing positive and negative words, and each has advantages and disadvantages.
For your scale, a measure of the central tendency of the words would be a fair measure, where the denominator is the number of scored words. This is a form of the "relative proportional difference" measure employed below. You would probably not want to divide the total sentiment words' scores by all words, since this makes each sentence's measure strongly affected by non-sentiment terms.
If you do not believe that the 11 point rating you describe is accurate, you could just classify it as positive or negative depending on its sign. Then you could apply the following methods where you have transformed
where each P and N refer to the counts of the Positive and Negative coded sentiment words, and O is the count of all other words (so that the total number of words = P + N + O).
Absolute Proportional Difference. Bounds: [0,1]
Sentiment = (P − N) / (P + N + O)
Disadvantage: A sentence's score is affected by non-sentiment-related content.
Relative Proportional Difference. Bounds: [-1, 1]
Sentiment = (P − N) / (P + N)
Disadvantage: A sentence's score may tend to cluster very strongly near the scale endpoints (because they may contain content primarily or exclusively of either positive or negative).
Logit scale. Bounds: [-infinity, +infinity]
Sentiment = log(P + 0.5) - log(N + 0.5)
This tends to have the smoothest properties and is symmetric around zero. The 0.5 is a smoother to prevent log(0).
For details, please see William Lowe, Kenneth Benoit, Slava Mikhaylov, and Michael Laver. (2011) "Scaling Policy Preferences From Coded Political Texts." Legislative Studies Quarterly 26(1, Feb): 123-155. where we compare their properties for measuring right-left ideology, but everything we discuss also applies to positive-negative sentiment.
you can use R tool for sentiment computation. here is the link you can refer to:
https://sites.google.com/site/miningtwitter/questions/sentiment/analysis
I was reading this question:
How to understand Locality Sensitive Hashing?
But then I found that the equation to calculate the cosine similarity is as follows:
Cos(v1, v2) = Cos(theta) = (hamming distance/signature length) * pi = ((h/b) * pi )
Which means if the vectors are fully similar, then the hamming distance will be zero and the cosine value will be 1. But when the vectors are totally not similar, then the hamming distance will be equal to the signature length and so we have cos(pi) which will result in -1. Shouldn't the similarity be always between 0 and 1?
Cosine similarity is the dot product of the vectors divided by the magnitudes, so it's entirely possible to have a negative value for the angle's cosine. For example, if you have unit vectors pointing in opposite directions, then you want the value to be -1. I think what's confusing you is the nature of the representation because the other post is talking about angles between vectors in 2-D space whereas it's more common to create vectors in a multidimensional space where the number of dimensions is customarily much greater than 2, and the value for each dimension is non-negative (e.g., a word occurs in document or not), resulting in a 0 to 1 range.
I have a simple set of data, 10 values that increase.
I want to fit them to a polynomial of the form:
Z = A1 + A2*X + A3*Y + A4*X^2 + A5*X*Y+ A6*Y^2
Where Z the output is the set of data above, A1 - A6 are the coefficients I am looking for,
X is the range of inputs (10 of course), and Y for the moment is a constant value.
How can I curve fit to this polynomial and not the standard 2nd order one that is created using 'trendline'?
Construct a Vandermonde matrix on your data points, find it's inverse with MINVERSE, then apply this to the vector of Z values with MMULT. This would work for polynomial degree n with n data points.
Otherwise you could try polynomial regression, which will again use the Vandermonde matrix.
More math than Excel really.