- #Sampletank 3 free serial number serial numbers#
- #Sampletank 3 free serial number serial number#
- #Sampletank 3 free serial number plus#
In some cases, conventional intelligence was used in conjunction with statistical methods, as was the case in estimation of Panther tank production just prior to D-Day.
In many cases, statistical analysis substantially improved on conventional intelligence. Panther tanks are loaded for transport to frontline units, 1943ĭuring the course of the Second World War, the Western Allies made sustained efforts to determine the extent of German production and approached this in two major ways: conventional intelligence gathering and statistical estimation.
N m e d ≈ 74.5 Historical example of the problem The Bayesian approach predicts that the median number of tanks produced will be very similar to the frequentist prediction: The frequentist approach predicts the total number of tanks produced will be:
#Sampletank 3 free serial number serial numbers#
In the SVG file, hover over a graph to highlight it.Īssuming tanks are assigned sequential serial numbers starting with 1, suppose that four tanks are captured and that they have the serial numbers: 19, 40, 42 and 60.
#Sampletank 3 free serial number serial number#
The example shows if four tanks are observed and the highest serial number is "60", frequentist analysis predicts 74, whereas Bayesian analysis predicts a mean of 88.5 and standard deviation of 138.72 − 88.5 = 50.22, and a minimum of 60 tanks.
#Sampletank 3 free serial number plus#
Bayesian analysis has solid yellow lines with mean and shading to show range from minimum possible value to mean plus 1 standard deviation). Frequentist analysis is shown with dotted lines. The number of observations in the sample is k. Additionally, regardless of a tank's date of manufacture, history of service, or the serial number it bears, the distribution over serial numbers becoming revealed to analysis is uniform, up to the point in time when the analysis is conducted.Įstimated population size (N). The adversary is presumed to have manufactured a series of tanks marked with consecutive whole numbers, beginning with serial number 1.
The problem is named after its historical application by Allied forces in World War II to the estimation of the monthly rate of German tank production from very limited data. Estimating the population maximum based on a single sample yields divergent results, whereas estimation based on multiple samples is a practical estimation question whose answer is simple (especially in the frequentist setting) but not obvious (especially in the Bayesian setting). The problem can be approached using either frequentist inference or Bayesian inference, leading to different results. A random sample of these items is taken and their sequence numbers observed the problem is to estimate N from these observed numbers.
In simple terms, suppose there exists an unknown number of items which are sequentially numbered from 1 to N. In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without replacement. During World War II, production of German tanks such as the Panther was accurately estimated by Allied intelligence using statistical methods