Final answer:
The best rationale for using smooth density estimators is to address the limitations of histograms, like their bin-sensitivity and lack of smoothness, providing a more consistent representation of data distribution. Therefore, the correct answer is option c) To overcome histogram's limitations such as the sensitivity to bin choice and non-smoothness.
Step-by-step explanation:
The best rationale to develop or use a smooth density estimator over a histogram is To overcome histogram's limitations such as the sensitivity to bin choice and non-smoothness. While both density estimators and histograms are used to approximate the distribution of data, histograms can be highly sensitive to how the data is binned.
This means that the choice of bin width and where the bin edges fall can significantly change the appearance of a histogram, which can lead to different interpretations of the data.
Smooth density estimators, on the other hand, provide a continuous curve, which is less sensitive to the exact values of the data points, offering a more stable and, typically, a better overall understanding of the data distribution.
The best rationale to develop or use a smooth density estimator over a histogram is option c) To overcome histogram's limitations such as the sensitivity to bin choice and non-smoothness.
A smooth density estimator, such as kernel density estimation, provides a continuous estimate of the underlying density function, whereas a histogram is based on discrete bins. This makes the smooth density estimator more flexible in representing the shape of the data distribution, especially when the data is not well-suited for discretization.
Additionally, smooth density estimators overcome the limitations of histograms in low dimensions, where histograms can become sensitive to the choice of bin width or boundaries.
Therefore, the correct answer is option c) To overcome histogram's limitations such as the sensitivity to bin choice and non-smoothness.