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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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Multiplicative Update Methods for Incremental Quantile Estimation.

Anis Yazidi, Hugo Hammer

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    Summary
    This summary is machine-generated.

    We developed a new, simple quantile estimator that is more efficient and accurate than existing methods. This lightweight, deterministic algorithm is easy to tune and performs well even when data distributions change over time.

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    Area of Science:

    • Computer Science
    • Statistics
    • Data Science

    Background:

    • Quantile estimation is crucial for understanding data distributions.
    • Existing methods like Tierney's estimator can be complex and computationally intensive.
    • There is a need for efficient and adaptable quantile estimators, especially for dynamic systems.

    Purpose of the Study:

    • To introduce a novel, lightweight incremental quantile estimator.
    • To offer an algorithm with reduced complexity and easier parameter tuning compared to existing methods.
    • To provide a deterministic and efficient solution for quantile estimation in time-varying distributions.

    Main Methods:

    • A novel lightweight incremental quantile estimation algorithm.
    • Deterministic updates with a subtly adjusted step size for convergence.
    • Proof of convergence using stochastic learning theory.

    Main Results:

    • The proposed estimator demonstrates significantly lower complexity than Tierney's estimator and its extensions.
    • The algorithm is easily tunable due to a single parameter, similar to the Frugal estimator.
    • Extensive experiments confirm superior performance compared to legacy algorithms.

    Conclusions:

    • The novel estimator offers a computationally efficient and accurate solution for quantile estimation.
    • Its deterministic nature and adaptability make it suitable for real-time and dynamic data analysis.
    • The proposed method represents a significant improvement over existing incremental quantile estimation techniques.