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Ranks01:02

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Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
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The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
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Optimal estimation of power Chris-Jerry distribution parameters using ranked set sampling design with application.

Ahmed R El-Saeed1, Amal S Hassan2, Mohammed Elgarhy3

  • 1Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia.

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Ranking set sampling (RSS) improves parameter estimation for the power Chris-Jerry distribution (PC-JD) compared to simple random sampling (SRS). Maximum likelihood estimation is highlighted as a beneficial strategy for both sampling methods.

Keywords:
Cramér-von Mises methodMinimum spacing square Linex distance methodPercentiles methodPower Chris-Jerry distributionRanked set sampling

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Area of Science:

  • Statistical modeling
  • Probability distributions
  • Sampling methodologies

Background:

  • Effective sample design is crucial for accurate parameter estimation.
  • Ranking set sampling (RSS) offers a cost-effective alternative to simple random sampling (SRS).
  • The power Chris-Jerry distribution (PC-JD) is a recent, versatile continuous lifetime distribution.

Purpose of the Study:

  • To investigate the application of RSS for estimating parameters of the PC-JD.
  • To compare the performance of various estimation methods under RSS and SRS.
  • To identify the most effective estimation strategy for PC-JD parameters using RSS.

Main Methods:

  • Utilized ranking set sampling (RSS) for parameter estimation.
  • Applied sixteen estimation techniques, including maximum likelihood, percentiles, minimum distance, Kolmogorov, and spacing methods.
  • Conducted simulation studies to assess accuracy measures and compare RSS with SRS.

Main Results:

  • Simulation results indicate RSS generally outperforms SRS in efficiency.
  • The maximum likelihood estimation method demonstrated strong performance for both RSS and SRS.
  • Partial and overall ranks identified optimal estimation strategies for survival data analysis.

Conclusions:

  • RSS is a more efficient sampling strategy than SRS for PC-JD parameter estimation.
  • Maximum likelihood estimation is a robust method for evaluating parameter estimates under both sampling schemes.
  • The study provides insights into optimal estimation techniques for survival data using RSS.