Abstract
Previous studies have shown that transmuting a standard distribution usually leads to a compound distribution with greater flexibility and performance. Following this fact, this article proposes a new extension of the normal distribution called “transmuted normal distribution”. The probability density function and cumulative distribution function of the transmuted normal distribution are defined by using the quadratic rank transmutation map. Also, a comprehensive study of some properties of the transmuted normal distribution is provided in this article. These properties include its moments, moment generating function, characteristics function, survival function, hazard function and distribution of order statistics. The maximum likelihood estimation of the unknown parameters is discussed. Three real life datasets have been used to determine whether the transmuted normal distribution is better than normal distribution or NOT and our results indicated that the transmuted normal model though flexible is NOT better than the conventional normal distribution.

Key words: Normal distribution, Transmutation map, Transmuted Normal, Properties, Reliability functions, Maximum likelihood estimation, Moments, order statistics, Applications