To generate a circular distribution, we use the alternate-wrapping technique (unlike the usual wrapping), by wrapping in the alternate directions, after each single-wrapping. The resulting distribution is called alternate-wrapped distribution. Some general properties and distinctions between the two wrapping schemes are indicated. As an illustration, alternate-wrapped-exponential distribution and alternate-wrapped-normal distribution are considered. The moment and maximum likelihood estimator of the parameters of alternative-wrapped-exponential distribution are obtained and their performance is evaluated using simulation. Maximum likelihood estimators are obtained for the parameters of the alternate-wrapped-normal distribution and simulation study is conducted, and this distribution is used to analyse a real-life data set and is compared with the wrapped normal distribution.
To generate a circular distribution, we use the alternate-wrapping technique (unlike the usual wrapping), by wrapping in the alternate directions, after each single-wrapping. The resulting distribution is called alternate-wrapped distribution. Some general properties and distinctions between the two wrapping schemes are indicated. As an illustration, alternate-wrapped-exponential distribution and alternate-wrapped-normal distribution are considered. The moment and maximum likelihood estimator of the parameters of alternative-wrapped-exponential distribution are obtained and their performance is evaluated using simulation. Maximum likelihood estimators are obtained for the parameters of the alternate-wrapped-normal distribution and simulation study is conducted, and this distribution is used to analyse a real-life data set and is compared with the wrapped normal distribution.