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Notice that lower bounds based on the MEs and L-MEs are smaller than the lower bound based on the MLEs. One of the most health-damaging pollutants is PM 2. (5) Burn-in 1,000 samples and compute the parameter of interest. 5 m), which can penetrate deep into the lungs. The expected values in the table also indicate that TLs based on the MEs and L-MEs are practically the same. One could assess this percentage by finding a 95% lower confidence limit for P(X80).

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As the sample size of 45 is considerably large, the CIs based on all three pivots are practically the same. On the other hand, we know that \(EF1\) when not all \(X_i\) are equal by the Cauchy inequality, thus \(1+A^2F+B^2E-2AB-EFA^2F+B^2E-2AB\). Our approach could aid environmentalists and policymakers to monitor air pollution in specific locations and give alarm signals when the air pollution level approaches a dangerous level. For example, a p content — coverage one-sided upper TL is the 100% upper confidence limit for the pth quantile of the population. Then the MLE of is given by
Let a^e and b^e be equivariant estimators of a and b, respectively.

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90,. Let X(1)X(r) be a set of failure times recorded from a sample of n test items. Yosboonruang, Niwitpong Niwitpong (2019) provided the confidence intervals for the CV of a lognormal distribution by utilizing Bayesian and fiducial GCI methods. Siddiqui [15] has go that the one-parameter Rayleigh distribution arises as an asymptotic distribution in some two-dimensional random walk problems. In addition, FCI and F-HPDCI produced similar results and performed well for small sample sizes. Our method can be called the “joint pivot method” as we obtain the confidence interval by uniting two pivots.

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However, the precisions of these three CIs could be different. Since the GCI approach was first introduced byWeerahandi (1993), several researchers have used it to provide statistical inferences (Tsui Weerahandi, 1989; Weerahandi, 1993; Weerahandi, 1995; Ye Wang, 2007; Krishnamoorthy Tian, 2008). We used 15,000 replications for each parameter combination. Let a~ denote the MLE of a thus obtained.

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In the Bangkok Metropolitan Region,Oanh et al. php) due to many factors contributing to PM 2. The
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will also be available for a limited time. Furthermore, the expected widths of the PIs based on the MLEs are slightly smaller than those based on the MEs and L-MEs for all the cases considered. These authors have also proposed credible sets for a function of the location and scale parameters using a gamma prior and a non-proper uniform prior.

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Furthermore,Chankham, Niwitpong Niwitpong (2019) recommended GCI for constructing confidence intervals for the coefficient of variation of an IG distribution; they found that GCI provide coverage probabilities greater than or equal to the nominal confidence level at 0. Algorithm 5. The 95% confidence intervals for the CV of this dataset by using the five methods are reported in Table this post From the cdf(2), it can be easily checked that the pth quantile of a two-parameter Rayleigh distribution is given by
Since the above quantile is the same form as the mean in(10) with c=qp(0,1), (qp(a,b)a^e)/b^e(qp(0,1)a^e)/b^e, where a^ and b^ are equivariant estimators based on a sample of size n from a Rayleigh(0,1) distribution.

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The MLE of can be obtained as ~=i=1n(Xia~)2/(2r), where a~ is the MLE of a. The properties of pivot-based procedures for type II censored samples should be similar to those of the complete sample case. Note that the pdf is defined only for ax, and so the MLE of a should maximize the profile likelihood function subject to the constraint that a is less than the smallest order statistic. 5 concentrations in the Bangkok Metropolitan Region over the course of a year and uncovered their key sources in the inner city adjacent to a busy road.