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The z score is calculated.\n * A positive enough z-score (ex. >1.96) indicates clustering,\n * while a negative enough z-score (ex. <-1.96) indicates a dispersed pattern.\n *\n * the z-score can be calculated based on a normal or random assumption.\n *\n * **Bibliography***\n *\n * 1. [Moran's I](https://en.wikipedia.org/wiki/Moran%27s_I)\n *\n * 2. [pysal](http://pysal.readthedocs.io/en/latest/index.html)\n *\n * 3. Andy Mitchell, The ESRI Guide to GIS Analysis Volume 2: Spatial Measurements & Statistics.\n *\n * @function\n * @param {FeatureCollection} fc\n * @param {Object} options\n * @param {string} options.inputField the property name, must contain numeric values\n * @param {number} [options.threshold=100000] the distance threshold\n * @param {number} [options.p=2] the Minkowski p-norm distance parameter\n * @param {boolean} [options.binary=false] whether transfrom the distance to binary\n * @param {number} [options.alpha=-1] the distance decay parameter\n * @param {boolean} [options.standardization=true] wheter row standardization the distance\n * @returns {MoranIndex}\n * @example\n *\n * const bbox = [-65, 40, -63, 42];\n * const dataset = turf.randomPoint(100, { bbox: bbox });\n *\n * const result = turf.moranIndex(dataset, {\n * inputField: 'CRIME',\n * });\n */\n\nfunction moranIndex(\n fc: FeatureCollection,\n options: {\n inputField: string;\n threshold?: number;\n p?: number;\n binary?: boolean;\n alpha?: number;\n standardization?: boolean;\n }\n): MoranIndex {\n const inputField = options.inputField;\n const threshold = options.threshold || 100000;\n const p = options.p || 2;\n const binary = options.binary ?? false;\n const alpha = options.alpha || -1;\n const standardization = options.standardization ?? true;\n\n const weight = spatialWeight(fc, {\n alpha,\n binary,\n p,\n standardization,\n threshold,\n });\n\n const y: number[] = [];\n featureEach(fc, (feature) => {\n const feaProperties = feature.properties || {};\n // validate inputField exists\n y.push(feaProperties[inputField]);\n });\n\n const yMean = mean(y);\n const yVar = variance(y);\n let weightSum = 0;\n let s0 = 0;\n let s1 = 0;\n let s2 = 0;\n const n = weight.length;\n // validate y.length is the same as weight.length\n for (let i = 0; i < n; i++) {\n let subS2 = 0;\n for (let j = 0; j < n; j++) {\n weightSum += weight[i][j] * (y[i] - yMean) * (y[j] - yMean);\n s0 += weight[i][j];\n s1 += Math.pow(weight[i][j] + weight[j][i], 2);\n subS2 += weight[i][j] + weight[j][i];\n }\n s2 += Math.pow(subS2, 2);\n }\n s1 = 0.5 * s1;\n\n const moranIndex = weightSum / s0 / yVar;\n const expectedMoranIndex = -1 / (n - 1);\n const vNum = n * n * s1 - n * s2 + 3 * (s0 * s0);\n const vDen = (n - 1) * (n + 1) * (s0 * s0);\n const vNorm = vNum / vDen - expectedMoranIndex * expectedMoranIndex;\n const stdNorm = Math.sqrt(vNorm);\n const zNorm = (moranIndex - expectedMoranIndex) / stdNorm;\n\n return {\n expectedMoranIndex,\n moranIndex,\n stdNorm,\n zNorm,\n };\n}\n\n/**\n * get mean of a list\n *\n * @private\n * @param {number[]} y\n * @returns {number}\n *\n */\nfunction mean(y: number[]): number {\n let sum = 0;\n for (const item of y) {\n sum += item;\n }\n return sum / y.length;\n}\n/**\n * get variance of a list\n *\n * @private\n * @param {number[]} y\n * @returns {number}\n *\n */\nfunction variance(y: number[]): number {\n const yMean = mean(y);\n let sum = 0;\n for (const item of y) {\n sum += Math.pow(item - yMean, 2);\n }\n return sum / y.length;\n}\n\nexport { moranIndex, MoranIndex };\nexport default moranIndex;\n"]}