A New Symmetric Bimodal Extension of Ailamujia Distribution: Properties and Application to Time Series Data

Abstract

A new symmetric bimodal extension of the Ailamujia distribution (SBEOAD) has been introduced in this study. pdf, cdf, survival function, hazard rate function, moments, absolute moments, mean residual life function, and quantile function were among the statistical characteristics of the distribution that were studied extensively. The maximum likelihood and method of moments approaches to estimating the SBEOAD's parameters were considered. The consistency property of the maximum likelihood estimates of the parameters has been empirically illustrated through a simulation investigation, The fits of the SBEOAD, the Laplace, Normal, and double Lindley distributions to two time series data were achieved using the maximum likelihood technique. When judged from the standpoint of the minimum AIC and BIC values, the SBEOAD provides the best fit to each of the data compared to the other three distributions fitted to the data.