Contents
We’ve covered a lot of ground and touched on the really interesting relationship between the Probability Density Function, Cumulative Distribution Function, and the Quantile Function. However, there are many questions still remaining regarding our parameter estimation problem, which we will continue to explore in the next post.
How is the CDF used in parameter estimation?
The CDF allows for quick and accurate estimates of the median (and other quantiles!) We can see that the median is very close to the Expectation of 0.0075. If we just need an approximate value we also can save all that integral work we did before for assessing the probability of ranges of values.
Is the quantile function the inverse of the CDF?
The Quantile Function. However mathematically the CDF takes an x and gives us f (x) = y, but in these cases we are actually estimating f (y) = x. What we have done visually is to compute the inverse of the CDF. The inverse of the CDF is an incredibly common and useful tool called the Quantile Function.
What is the true conversion rate of the CDF?
The distance between them is the approximate integral. Integration has never been so easy! Eyeballing the CDF we can see that on the y-axis these values range from roughly 0.5 to 0.99, meaning that there is roughly a 49% chance that our true conversion rate lies somewhere between these two values.
What’s the difference between a percentile and a quantile?
Percentiles and Quantiles. The k-th percentile of a set of values divides them so that k% of the values lie below and (100−k)% of the values lie above. • The 25th percentile is known as the lower quartile. • The 50th percentile is known as the median. • The 75th percentile is known as the upper quartile.
Why do we use a quantile based plot?
• Quantile-quantile plots allow us to compare the quantiles of two sets of numbers. • This kind of comparison is much more detailed than a simple comparison of means or medians. • There is a cost associated with this extra detail. We need more observations than for simple comparisons.