The best replacement for normal distribution is standard normal distribution.

The best alternatives to normal distribution are rated as following:

★★★★★	standard normal distribution
★★★★	t distribution
★★★★	uniform distribution
★★★	binomial distribution
★★	skewed
★★	bell curve
★★	poisson
★★	normal curve
★★	gaussian
★★	binomial
★	exponential distribution
★	gaussian distribution
★	t-distribution
★	sampling distribution
★	normal distribution
★	poisson distribution
★	sample distribution
★	power law distribution
★	curve
★	skewed distribution
★	standard deviation
	bell shaped curve
	non normal distribution
	log normal distribution
	lognormal distribution
	modified normal distribution
	exponential
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	student t
	frequency distribution
	central limit theorem
	gamma distribution
	other distribution
	standard distribution

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Speaking about normal distribution, one probably shouldn't forget about standard deviation.

Other search terms related to normal distribution and their ratings are:

★★★★★	standard deviation
★★★	mean and standard deviation
★	probability
★	percentiles
	z scores

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normal distribution

standard normal distribution

t distribution