Function estimate_lambda 

pub fn estimate_lambda(
    y: &[f64],
    lambda_min: f64,
    lambda_max: f64,
) -> Result<LambdaEstimate, TransformError>

Estimate the optimal Box-Cox λ via maximum likelihood.

Maximises the profile log-likelihood:

ℓ(λ) = -(n/2)·ln(Var_population(y(λ))) + (λ-1)·Σ ln(yᵢ)

using a golden-section search over [lambda_min, lambda_max] with up to 100 iterations (terminating early when the bracket width < 1e-6).

The result says whether the maximum was found on an end of the range (LambdaEstimate::at_bound): a λ of lambda_max because the likelihood peaks there is indistinguishable by value from one where the likelihood keeps rising past it, and only the latter means the range cut the search short.

Errors

• TransformError::InvalidLambdaRange — lambda_min >= lambda_max, or either bound is not finite
• TransformError::InsufficientData — fewer than 2 data points
• TransformError::NonPositiveData — any element ≤ 0
• TransformError::NonFiniteData — any element is NaN or infinite

Examples

use u_numflow::transforms::estimate_lambda;

// Exponential data is well-linearised by log (λ ≈ 0).
let y: Vec<f64> = (1..=30).map(|i| (i as f64 * 0.2_f64).exp()).collect();
let est = estimate_lambda(&y, -2.0, 2.0).unwrap();
assert!(est.lambda.abs() < 0.3, "expected lambda near 0, got {}", est.lambda);
assert!(!est.at_bound);