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Particle Swarm Optimization (PSO) has been frequently employed to solve diversified optimization problems. Choosing initial placement for population plays an important role in meta-heuristic methods since they can significantly converge. In this study, probability distribution has been introduced to enhance the diversity of swarm and convergence speed. Population initialization method based on uniform distribution is normally used when there is no preceding knowledge available regarding the candidate solution. In this paper, a new approach to initialize population is proposed using probability sequence Weibull marked as (WI-PSO) that applies the probability distribution to generate numbers at random locations for swarm initialization. The proposed method (WI-PSO) is tested on sixteen well-known uni-modal and multi-modal benchmark test functions broadly adopted by the research community and its encouraging performance is investigated and compared with the Exponential distribution based PSO (E-PSO), Beta distribution based PSO (BT-PSO), Gamma distribution based PSO (GA-PSO) and Log-normal distribution based PSO (LN-PSO). Artificial Neural Networks (ANNs) have become the most powerful tool for classification of complex benchmark problems. We have experimented the proposed method (WI-PSO) for weight optimization of a feed-forward neural network to ensure its purity and have compared with conventional back-propagation algorithm (BPA), E-PSO, BT-PSO, GA-PSO and LN-PSO. Due to flexible behaviour in the degree of freedom, the experimental results infer the perfection and dominance of the Weibull based population initialization. The result exhibits the anticipation of influence exerted by the proposed technique on all sixteen objective functions and eight real-world benchmark data sets.