On Some Length-Biased Weighted Weibull Distribution
نویسندگان
چکیده
In this paper, we develop the length-biased form of the weighted Weibull distribution (WWD) named as length-biased weighted Weibull distribution (LBWWD). Well known distributions are generated by expanding suitable function of the parameters. Shape of the distribution is studied in detail. Various properties of length-biased WWD are discussed. Newby’s method along with method of moment has been used to estimate the parameters of the length-biased WWD. To justify the use of LBWWD; LBWWD is fitted to 30 consecutive year’s data from 1981 2010 of June rainfall (in mm) of Tezpur, Assam, India.
منابع مشابه
Fisher Information in Weighted Distributions
Standard inference procedures assume a random sample from a population with density fθ(x) for estimating the parameter θ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ≥ 0, and constructed a weighted distribution with a density f θ (x) that is proportional to w(x)fθ(x). In this paper, we ...
متن کاملLength Bias in the Measurements of Carbon Nanotubes
To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and as a result, the sample is length biased. The selection bias model can be demonstrated through Buffon's Needle Problem, which was extended to general curves that more realistically repre...
متن کاملSome Statistical Inferences on the Parameters of Records Weibull Distribution Using Entropy
In this paper, we discuss different estimators of the records Weibull distribution parameters and also we apply the Kullback-Leibler divergence of survival function method to estimate record Weibull parameters. Finally, these estimators have been compared using Monte Carlo simulation and suggested good estimators.
متن کاملEstimation Parameter of R = P(Y < X) for Length-Biased Weighted Lomax Distributions in the Presence of Outliers
The concept of length-biased distribution is applied in expending proper models for lifetime data. The length-biased distribution is a special case of well-known weighted distribution. In this article, we introduce a length-biased weighted Lomax distribution (LBWLD) with k presence of outliers and estimate the parameter of R = P(Y < X) when the random variables X and Y are independent and have ...
متن کاملBias in the Weibull Strength Estimation of a SiC Fiber for the Small Gauge Length Case∗
It is known that the single-modal Weibull model describes well the size effect of brittle fiber tensile strength. However, some ceramic fibers have been reported that single-modal Weibull model provided biased estimation on the gauge length dependence. A hypothesis on the bias is that the density of critical defects is very small, thus, fracture probability of small gauge length samples distrib...
متن کامل