I was reading about distribution in statistics. I came across this idea that there is difference between Normal distribution and bell shape or mound shape distributions. I do not get it. Are they not the same? Anyone with short explanation. Thank you.
"Bell-shaped" is a figure of speech. In fact, my meditation bell is not "bell-shaped" at all! There is no mathematical definition of a bell. All we can say is that the normal distribution has a shape a bit like a bell. But other symmetrical distributions also have bell-like shapes. The t-distribution, for example
https://en.wikipedia.org/wiki/Student%27s_t-distribution
Normal distribution is actually a symmetric distribution with mean ,median and mode all lying at the same point.The graph of normal distribution is actually a mesokurtic curve which resembles the shape of a bell.
So bell shaped is basically a terminology used for our better understanding of the nature and shape of the curve.Generally symmetric distributions are bell shaped like t dist can be another example.
Any symmetric distribution is bell-shaped. The tail behaviour is a key point that distinguishes others from normal. e.g. Cauchy distribution is a very heavy tailed one,"bell-shaped" distribution that puts more mass at both tails than a normal should.
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