Application of Burrxii- Dal and Weibull-Dal Distribution: A Case Study of Rice Yield in Gujranwala and Sheikhupura Pakistan - Nawaz, Shahbaz; Md Yusof, Zahayu; Friday Zinzendoff, Okwonu (Ashwin Anokha Publications & Distributions, 2021)
Background: In statistical theory; the development of new models is necessary that are helpful in describing and producing innovative distributions. BurrXII-DAL and Weibull-DAL distribution are the two models that are used for estimating the failure rate, dependability, and acceptability sampling plans along with the distribution of the data. Objective:“The objective of the study was to modified new models, investigate the properties of the models along with the estimation of the maximum likelihood of the parameters”. Methods: The study was conducted to determined the property of BurrXII-DAL and Weibull-DAL distribution with the help of five parameters according to the maximum likelihood and the distributions of the two sets of the real data were inspected against the three and two parameters. Exponential Generalized Power Weibull (EGPW), Nadarajah Haghighi (NH), and Kumaraswamy Generalized Power Weibull (KwGPW) distributions were compared with the proposed model. The real data set of rice yield per acre was analyzed by using BURXII-DAL and Weibull-DAL models for the further description of parameters. The analysis was done by using R packages and the square mean was used for the analysis of the approximation of the shape of parameters. Result: The results of the study showed that BXII-DAL performs better than the other models having maximizing the distribution with maximum MLE’s and α (0.0300), β ( 2.7272) and λ 5.7469. Similarly; The statistics W^*, A^*, K-S, p-value, AIC, BIC and l ̂ of BXII-DAL showed that AIC has the final value of 861.3306 while BIC with final value of 872.7139. MLE and standard error of W-DAL model showed better and smaller leading towards smaller variation among values with α (0.1343), β (4.7917) and λ (0.0991). The value of AIC, A^*and W^* for W-DAL statistic showed that AIC had the final value of 505.395 while BIC had final value of 516.778. Conclusion: BurrXII-DAL and Weibull-DAL models are good proposed models among competitive models to the data set and can be highly effective for future analysis as both MLE values showed smaller variation as compared to other models with smaller standard errors