Estimation of the parameter of model in climate change under record values based on record ranked set sampling scheme

There are many applied experiments that, for unknown reasons, have a disappeared observations. Some of these limitations are: little opportunity to announce the results. not having access to all the units or being disappointed with the result of all the units. These factors cause the researcher may not have access to all the studied data. There are some experiments where have been done sequentially, and only record-breaking data are observed. These types of data have been used in a wide variety of practical experiments, such as oil and mining surveys, quality control, hydrology, sports achievements, seismology, the strength of materials, economics, industry, and climatology. An observation is called an upper record valueif its value exceeds all previous observations. An analogous definition can be given for lower record value. The record ranked set sample (RRSS) scheme, has been formally proposed by Salehi and Ahmadi, 2014 . Among the authors who worked on this scheme, Salehi and Ahmadi (2015) considered the estimation of stress and strength using upper RRSS from the exponential distribution. They also, with the collaborationof Dey (2016), made a comparison between RRSS scheme and the ordinary record statistics in estimating the unknown parameter of the proportional hazard rate model. They showed that the RRSS scheme outperforms the ordinary record statistics in the frequentist/Bayesian point and interval estimation under that family of distributions. Safaryian et al. (2019) proposed some improved estimators, including the preliminary test estimator, as well as a stein-type shrinkage estimator for stress-strength reliability using record ranked set sampling scheme. Recently, Sadeghpour et al. (2020) considered the estimation of stress and strength reliability using a lower record ranked set sampling scheme under the generalized exponential distribution. To introduce lower RRSS scheme, suppose we have n independent random sequences where the ith sequence sampling is stopped whenever the ith lower record is observed. The only observations available for analysis are the last lower record value in each sequence. This process is called lower record ranked set sampling scheme or (RRSS). Among the authors who worked on this scheme, Ahsanullah (1995), Arnold et al. (1998), Paul and Thomas (2017) , Salehi et al (1998) , Nevzorov (2001) and Gulati and Padgett (2003). Nowadays, climatic factors directly affect human life. Therefore, to different planning, the role of the parameters of climatic as an influencing factor in the execution process of the plans is worthwhile. One of the important aims of climatology, is to get an estimate of the unknown parameters of model. In such situations, considering appropriate estimators and sampling schemes, in order to reduce the cost and increase the accuracy based on information from the sample are important. In this research, based on RRSS scheme, the problem of Bayes estimation and maximum likelihood estimation of the parameter of generalized exponential model is studied. The Bayesian approach, as an alternative to the classical approach, is in statistical inference. Its principle is to incorporate the information in the parameters’ history through a prior distribution assuming, a known form of distribution. The parameters of a prior distribution called prior parameters. In the Bayesian inference, the performance of the estimator depends on the prior distribution and also on the loss function used. A symmetric loss as Square error loss function is found in different fields. The symmetric nature of this function gives equal weight to overestimation as well as underestimation, while in the estimation of parameters of lifetime model, overestimation may be more severe than underestimation or vice-versa. An asymmetric loss function, is also useful. For example, in the estimation of reliability and failure rate function, an overestimation is usually much more serious than underestimate .Using a Monte Carlo simulation, for both estimation methods, namely Bayes estimation and maximum likelihood estimation, the risk criterion estimators are computed and evaluated. Finally, the results are checked by analyzing real data of temperature ‎record ‎values‎ related to on a daily time scale from the month of January during the years 2018 to 2021 which were obtained from the meteorological station of Sari city in Mazandaran province. The results demonstrate the Bayes estimates are generally, better than the maximum likelihood estimates, and all estimates improve by increasing record values. It is recommended to use the RRSS scheme if conditions are ready for the RRSS scheme.