Statistics of sinc function with normal argument

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The discussion focuses on finding the probability density function (PDF), cumulative distribution function (CDF), and moments of the sinc function defined as y = sinc(x) = sin(pi*x)/(pi*x) where x follows a normal distribution N(0,s^2). Calculating the CDF and PDF is noted to be challenging due to the non-one-to-one nature of the sinc function. However, it is suggested that the moments can be derived through numerical integration or potentially analytically using complex variable techniques. The conversation highlights the complexities involved in statistical analysis of the sinc function under a normal argument. Overall, the topic emphasizes the mathematical intricacies of the sinc function in probability theory.
rhz
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Hi,

Can anyone point me to the pdf, cdf, moments, etc of

y = sinc(x) = sin(pi*x)/(pi*x) where x ~ N(0,s^2)?

Thanks!
 
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The CDF and PDF will be tricky to calculate because sinc is not one-to-one.

However the moments could be calculated by numerical integration and possibly even analytically using complex variable methods.
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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