Current Science Research Bulletin

The contaminated normal distribution is the distribution of the normal random variable mixed with other random variables. The combination of the other random variables can be either the discrete random variable or the continuous random variable. The normal random variable is the main random variable, while the other random variable is follower random variables. The purpose of this study is to determine the cumulative distribution function and the probability density function of the contaminated standard normal random variable. In addition, it also seeks the properties of the contaminated standard normal random variable. The contaminated normal discusses random variables constructed by the standard normal random variable and the discrete random variable. The contaminated normal is expanded in the form of the linear contaminated normal. The mean of the contaminated normal is zero, while the variance of the contaminated normal is a constant. If the contaminated normal random variable is a linear function, then the mean of the linear contaminated normal is equal intercept, but the variance of the linear contaminated normal is a function of the square of the slope. The properties of the contaminated standard normal random variable are the center point of the data at the mean, the variance is a constant, the shape of the curve is bell-shaped, the data distribution is symmetric, and the axis of symmetry is at the mean of the contaminated standard normal random variable.

Contaminated Normal Distribution, Mixture Distribution, Bell-shaped, Symmetric

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