In this paper, we introduce a new continuous distribution mixing exponential and gamma distributions, called new Sushila distribution. We derive some properties of the distribution include: probability density function, cumulative distribution function, expected value, moments about the origin, coefficient of variation (C.V.), coefficient of skewness, coefficient of kurtosis, moment generating function, and reliability measures. The distribution includes, a special cases, the Sushila distribution as a particular case p=1/2 (θ = 1). The hazard rate function exhibits increasing. The parameter estimations as the moment estimation (ME), the maximum likelihood estimation (MLE), nonlinear least squares methods, and genetic algorithm (GA) are proposed. The application is presented to show that model to fit for waiting time and survival time data. Numerical results compare ME, MLE, weighted least squares (WLS), unweighted least squares (UWLS), and GA. The results conclude that GA method is better performance than the others for iterative methods. Although, ME is not the best estimate, ME is a fast estimate, because it is not an iterative method. Moreover, The proposed distribution has been compared with Lindley and Sushila distributions to a waiting time data set. The result shows that the proposed distribution is performing better than Lindley and Sushila distribution.

Regression analysis is a statistical approach used to investigate the correlations between variables, especially linear regression, that is a simple but effective approach for analyzing the relationship between a dependent variable and one independent variable. Since it has limitations based on the assumption that the mean of the noise should be zero, there are still some areas where it may be improved. In this article, we introduce a novel data fitting algorithm called the pulling linear regression, which is separated into two types: the line-pulling linear regression and the band-pulling linear regression. The method is developed from linear regression, which can create the regression line from the function that uses noise with various distributions. The result demonstrates that the sequence of sum square errors of the pulling linear regression is convergent. Moreover, we have a numerical example to show that the performance of the proposed algorithm is better than that of linear regression when the mean of the noise is not zero. And the last, we have an application to smooth the boundary of the pectoral muscle in digital mammograms. We found that the regression line of the proposed algorithm can do better than the linear regression when we would like to remove only the muscle part.

In this paper, we propose a method for estimating Normal distribution parameters using genetic algorithm. The main purpose of this research is to identify the most efficient estimators among three estimators for Normal distribution; Maximum likelihood method (ML), the least square method (LS), and genetic algorithm (GA) via numerical simulation and three real data, carbonation depth of Concrete Girder Bridges data examples which are based on performance measures such as The Root Mean Square Error (RMSE), Kolmogorov-Smirnov test, and Chi squared test. The simulation studies are conducted to evaluate the performances of the proposed estimators and provide statistical analysis of the real data set. The numerical results, x^2, show that the genetic algorithm performs better than other methods for actual data and simulated data unless the sample size is small.

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