What does ua mean?

The definition of unilateral quantile is as follows: if p {x >；; Ua}=a, then UA is called the upper a quantile of X.

Bilateral quantile is defined as follows: P{|X| >Ua/2}=a, then Ua/2 is the bilateral quantile of X.

For standard normal distribution:

As can be seen from the definition, the unilateral quantile Ua is also a bilateral quantile. By p {x & gtua} = a.

Available P{|X| >Ua}=2a, which means that UA is only a bilateral 2a qUantile.

As can be seen from the definition, the bilateral quantile Ua/2 is also the unilateral quantile a/2.

brief introduction

The normal curve is bell-shaped, with low ends and high middle, which is symmetrical left and right, so people often call it bell-shaped curve.

If the random variable X obeys the normal distribution with a mathematical expectation of μ and a variance of σ2, it is recorded as N(μ, σ2). The expected value μ of probability density function with normal distribution determines its position, and its standard deviation σ determines its distribution amplitude. When μ = 0 and σ = 1, the normal distribution is standard normal distribution.